Tổng các số chia hết cho 3 trong C++

Chương trình C# để tính tổng của tất cả các số chia hết cho 3 trong phạm vi đã cho

Mã số

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

 

tĩnh void Chính(chuỗi[] args)

        {

            int sum = 0;

            Bảng điều khiển. Viết("Số 1. ");

            int num1 = Chuyển đổi.ToInt32(Bảng điều khiển. Dòng đọc());

            Bảng điều khiển. Viết("Số 2. ");

            int num2 = Chuyển đổi.ToInt32(Bảng điều khiển. Dòng đọc());

            cho(int i=num1;i<=num2;i++)

            {

                        nếu(i%3==0)

                {

                    tổng += i;

                }

            }

            Bảng điều khiển. WriteLine("Tổng các số " +sum);

            Bảng điều khiển. ReadKey();

        }

 

đầu ra

Tổng các số chia hết cho 3 trong C++

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Như thế này

Thích Đang tải.

Cho ba số A, B, M sao cho A < B, nhiệm vụ là tìm tổng các số chia hết cho M trong khoảng [A, B]

ví dụ.  

Đầu vào. A = 25, B = 100, M = 30
đầu ra. 180
Giải trình.  
Trong khoảng [25, 100] 30, 60 và 90 là các số chia hết cho M = 30
Do đó, tổng của những con số này = 180

Đầu vào. A = 6, B = 15, M = 3
đầu ra. 42
Giải trình.  
Trong khoảng [6, 15] 6, 9, 12 và 15 là các số chia hết cho M = 3.  
Do đó, tổng của những số này = 42.  

Khuyến khích. Vui lòng thử cách tiếp cận của bạn trên {IDE} trước, trước khi chuyển sang giải pháp

Cách tiếp cận ngây thơ. Kiểm tra xem mỗi số trong dãy [A, B] có chia hết cho M hay không. Và cuối cùng, cộng tất cả các số chia hết cho M

Dưới đây là việc thực hiện các phương pháp trên.  

C++




// C++ program to find the sum of numbers

// divisible by M in the given range

 

#include <bits/stdc++.h>

using

M, 2M, 3M, ...
0
M, 2M, 3M, ...
1

 

M, 2M, 3M, ...
2

// divisible by M in the given range

M, 2M, 3M, ...
4
M, 2M, 3M, ...
5_______0_______4
M, 2M, 3M, ...
7
M, 2M, 3M, ...
4
M, 2M, 3M, ...
9
M, 2M, 3M, ...
4
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
7

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
9

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
3
N = B / M - (A - 1)/ M
4
M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
6

 

N = B / M - (A - 1)/ M
7_______20_______8

N = B / M - (A - 1)/ M
7_______29_______0

N = B / M - (A - 1)/ M
7_______29_______2
sum = N * ( (first term + last term) / 2)
3

sum = N * ( (first term + last term) / 2)
4_______29_______5

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9
42
0

42
1

 

42
2

M, 2M, 3M, ...
4
42
4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
42
7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
42
9

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4 // C++ program to find the sum of numbers2

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____687_______4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____687_______6

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9 // C++ program to find the sum of numbers9

42
1

Java




// divisible by M in the given range1

// divisible by M in the given range

// divisible by M in the given range3 // divisible by M in the given range4

 

// divisible by M in the given range5 // divisible by M in the given range6

// divisible by M in the given range7

M, 2M, 3M, ...
2

// divisible by M in the given range

#include <bits/stdc++.h>0

M, 2M, 3M, ...
4
M, 2M, 3M, ...
5_______0_______4
M, 2M, 3M, ...
7
M, 2M, 3M, ...
4
M, 2M, 3M, ...
9
M, 2M, 3M, ...
4
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4 using4using5using6

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
9

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
3
N = B / M - (A - 1)/ M
4
M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
6

// divisible by M in the given range7

N = B / M - (A - 1)/ M
7_______20_______8

N = B / M - (A - 1)/ M
7_______29_______0

N = B / M - (A - 1)/ M
7_______29_______2
M, 2M, 3M, ...
14using5
M, 2M, 3M, ...
16

sum = N * ( (first term + last term) / 2)
4_______29_______5

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9
42
0

42
1

// divisible by M in the given range7

42
2

M, 2M, 3M, ...
28 #include <bits/stdc++.h>0
M, 2M, 3M, ...
30
M, 2M, 3M, ...
31

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
42
7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
42
9

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
M, 2M, 3M, ...
39
M, 2M, 3M, ...
40
M, 2M, 3M, ...
41
M, 2M, 3M, ...
42
M, 2M, 3M, ...
43
M, 2M, 3M, ...
44using6

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____687_______4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
50_______0_______51
M, 2M, 3M, ...
52

42
1

42
1

 

M, 2M, 3M, ...
55

Python3




M, 2M, 3M, ...
56

M, 2M, 3M, ...
57

 

M, 2M, 3M, ...
58

M, 2M, 3M, ...
57

M, 2M, 3M, ...
60
M, 2M, 3M, ...
61

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
63

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
65
M, 2M, 3M, ...
66 using5

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
69

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
71

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
3
M, 2M, 3M, ...
74_______0_______75
M, 2M, 3M, ...
76
M, 2M, 3M, ...
77
M, 2M, 3M, ...
78
M, 2M, 3M, ...
79_______0_______80

 

N = B / M - (A - 1)/ M
7_______0_______82

N = B / M - (A - 1)/ M
7_______0_______84

N = B / M - (A - 1)/ M
7_______29_______2
M, 2M, 3M, ...
87_______0_______88
M, 2M, 3M, ...
89
M, 2M, 3M, ...
66
M, 2M, 3M, ...
66 using5
M, 2M, 3M, ...
80

sum = N * ( (first term + last term) / 2)
4_______0_______65
M, 2M, 3M, ...
78
M, 2M, 3M, ...
66
M, 2M, 3M, ...
74

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
00

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9
M, 2M, 3M, ...
65

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
04

sum = N * ( (first term + last term) / 2)
2
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
06
M, 2M, 3M, ...
66
M, 2M, 3M, ...
66
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
09
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
10

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
13

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
15

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
17
M, 2M, 3M, ...
66
M, 2M, 3M, ...
40

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
21
M, 2M, 3M, ...
66
M, 2M, 3M, ...
42

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
89
M, 2M, 3M, ...
66
M, 2M, 3M, ...
44

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
29

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
31
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
32

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
34

C#




K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
35

// divisible by M in the given range

using

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
38

 

// divisible by M in the given range5 // divisible by M in the given range6

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
41

M, 2M, 3M, ...
2

// divisible by M in the given range

#include <bits/stdc++.h>0

M, 2M, 3M, ...
4
M, 2M, 3M, ...
5_______0_______4
M, 2M, 3M, ...
7
M, 2M, 3M, ...
4
M, 2M, 3M, ...
9
M, 2M, 3M, ...
4
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
41

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
9

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
3
N = B / M - (A - 1)/ M
4
M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
6

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
41

N = B / M - (A - 1)/ M
7_______20_______8

N = B / M - (A - 1)/ M
7_______29_______0

N = B / M - (A - 1)/ M
7_______29_______2
sum = N * ( (first term + last term) / 2)
3

sum = N * ( (first term + last term) / 2)
4_______29_______5

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
41

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9
42
0

42
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
41

42
2

M, 2M, 3M, ...
28 #include <bits/stdc++.h>0
M, 2M, 3M, ...
30
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
91

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
42
7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
42
9

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4 // C++ program to find the sum of numbers2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
41

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____687_______4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
04
M, 2M, 3M, ...
51
M, 2M, 3M, ...
52

42
1

42
1

// divisible by M in the given range7

N = B / M - (A - 1)/ M
10

Javascript




N = B / M - (A - 1)/ M
11

 

N = B / M - (A - 1)/ M
12

// divisible by M in the given range

 

M, 2M, 3M, ...
2

// divisible by M in the given range

N = B / M - (A - 1)/ M
16
N = B / M - (A - 1)/ M
17

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
23
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
7

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
9

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
3
N = B / M - (A - 1)/ M
4
N = B / M - (A - 1)/ M
23
N = B / M - (A - 1)/ M
6

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3

N = B / M - (A - 1)/ M
7_______20_______8

N = B / M - (A - 1)/ M
7_______29_______0

N = B / M - (A - 1)/ M
7_______29_______2
sum = N * ( (first term + last term) / 2)
3

sum = N * ( (first term + last term) / 2)
4_______29_______5

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9
42
0

42
1

 

42
2

 

42
7

42
9

N = B / M - (A - 1)/ M
23 // C++ program to find the sum of numbers2

 

// C++ program to find the sum of numbers4

N = B / M - (A - 1)/ M
56

 

N = B / M - (A - 1)/ M
57

 

N = B / M - (A - 1)/ M
58

đầu ra.

42

 

Thời gian phức tạp. O(B-A)
Không gian phụ trợ. Ô(1)

Phương pháp tiếp cận hiệu quả. Ý tưởng là sử dụng khái niệm Cấp số cộng và chia hết.  

  • Khi trực quan hóa, bội số của M có thể được nhìn thấy để tạo thành một chuỗi
M, 2M, 3M, ...
  • Nếu chúng ta có thể tìm thấy giá trị của K là số hạng đầu tiên trong phạm vi [A, B] chia hết cho M, thì một cách trực tiếp, chuỗi sẽ là
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
  • Do đó, thuật ngữ 'K' đầu tiên trong chuỗi không là gì ngoài số lớn nhất nhỏ hơn hoặc bằng A chia hết cho M
  • Tương tự số hạng cuối cùng là số nhỏ nhất lớn hơn hoặc bằng B chia hết cho M
  • Tuy nhiên, nếu bất kỳ số nào ở trên vượt quá phạm vi, thì chúng ta có thể trừ trực tiếp M từ nó để đưa nó vào phạm vi
  • Và, số các số hạng chia hết cho M có thể được tìm ra bởi công thức
N = B / M - (A - 1)/ M
  • Do đó, tổng của các yếu tố có thể được tìm ra bởi
sum = N * ( (first term + last term) / 2)

Dưới đây là việc thực hiện các phương pháp trên.  

C++




// C++ program to find the sum of numbers

// divisible by M in the given range

 

#include <bits/stdc++.h>

using

M, 2M, 3M, ...
0
M, 2M, 3M, ...
1

 

N = B / M - (A - 1)/ M
65

N = B / M - (A - 1)/ M
66

N = B / M - (A - 1)/ M
67

M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
69_______0_______4
N = B / M - (A - 1)/ M
71_______0_______4
N = B / M - (A - 1)/ M
73

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
76

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
78

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
81

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
83

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
85

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2
N = B / M - (A - 1)/ M
88

N = B / M - (A - 1)/ M
7_______29_______9
N = B / M - (A - 1)/ M
91

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
93

 

N = B / M - (A - 1)/ M
7_______20_______95

N = B / M - (A - 1)/ M
7_______20_______97

N = B / M - (A - 1)/ M
7_______20_______99

N = B / M - (A - 1)/ M
7_______29_______9
sum = N * ( (first term + last term) / 2)
02

42
1

 

sum = N * ( (first term + last term) / 2)
04

sum = N * ( (first term + last term) / 2)
05

N = B / M - (A - 1)/ M
67

M, 2M, 3M, ...
4
sum = N * ( (first term + last term) / 2)
08
M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
71_______0_______4
N = B / M - (A - 1)/ M
73

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
76

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
78

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
sum = N * ( (first term + last term) / 2)
20

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
83

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
85

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2
N = B / M - (A - 1)/ M
88

N = B / M - (A - 1)/ M
7_______29_______9
N = B / M - (A - 1)/ M
91

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
93

 

N = B / M - (A - 1)/ M
7_______20_______95

N = B / M - (A - 1)/ M
7_______20_______97

N = B / M - (A - 1)/ M
7_______20_______99

N = B / M - (A - 1)/ M
7_______29_______9
sum = N * ( (first term + last term) / 2)
41

42
1

 

M, 2M, 3M, ...
2

// divisible by M in the given range

M, 2M, 3M, ...
4
M, 2M, 3M, ...
5_______0_______4
M, 2M, 3M, ...
7
M, 2M, 3M, ...
4
M, 2M, 3M, ...
9
M, 2M, 3M, ...
4
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
sum = N * ( (first term + last term) / 2)
61

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
sum = N * ( (first term + last term) / 2)
64

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
66

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
68

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2
sum = N * ( (first term + last term) / 2)
71

N = B / M - (A - 1)/ M
7_______29_______73

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2
sum = N * ( (first term + last term) / 2)
76

N = B / M - (A - 1)/ M
7_______29_______78

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
80

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
sum = N * ( (first term + last term) / 2)
83

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
85

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9
sum = N * ( (first term + last term) / 2)
88

42
1

 

42
2

M, 2M, 3M, ...
4
42
4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
95

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
42
9

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4 // C++ program to find the sum of numbers2

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____687_______4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
42
04

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9 // C++ program to find the sum of numbers9

42
1

Java




// divisible by M in the given range1

// divisible by M in the given range

 

 

// divisible by M in the given range5 // divisible by M in the given range6

// divisible by M in the given range7

N = B / M - (A - 1)/ M
65

N = B / M - (A - 1)/ M
66

N = B / M - (A - 1)/ M
67

#include <bits/stdc++.h>0

M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
69_______0_______4
N = B / M - (A - 1)/ M
71
M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
73

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
76

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
78

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
81

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
83

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
85

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2
42
39using5
M, 2M, 3M, ...
16

N = B / M - (A - 1)/ M
7_______29_______9
N = B / M - (A - 1)/ M
91

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
93

// divisible by M in the given range7

N = B / M - (A - 1)/ M
7_______20_______95

N = B / M - (A - 1)/ M
7_______20_______97

N = B / M - (A - 1)/ M
7_______20_______99

N = B / M - (A - 1)/ M
7_______29_______9
sum = N * ( (first term + last term) / 2)
02

42
1

// divisible by M in the given range7

sum = N * ( (first term + last term) / 2)
04

sum = N * ( (first term + last term) / 2)
05

N = B / M - (A - 1)/ M
67

#include <bits/stdc++.h>0

M, 2M, 3M, ...
4
sum = N * ( (first term + last term) / 2)
08_______0_______4
N = B / M - (A - 1)/ M
71
M, 2M, 3M, ...
4
N = B / M - (A - 1)/ M
73

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
76

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
78

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
sum = N * ( (first term + last term) / 2)
20

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
83

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
85

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2
42
39using5
M, 2M, 3M, ...
16

N = B / M - (A - 1)/ M
7_______29_______9
N = B / M - (A - 1)/ M
91

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
93

// divisible by M in the given range7

N = B / M - (A - 1)/ M
7_______20_______95

N = B / M - (A - 1)/ M
7_______20_______97

N = B / M - (A - 1)/ M
7_______20_______99

N = B / M - (A - 1)/ M
7_______29_______9
sum = N * ( (first term + last term) / 2)
41

42
1

// divisible by M in the given range7

M, 2M, 3M, ...
2

// divisible by M in the given range

#include <bits/stdc++.h>0

M, 2M, 3M, ...
4
M, 2M, 3M, ...
5_______0_______4
M, 2M, 3M, ...
7
M, 2M, 3M, ...
4
M, 2M, 3M, ...
9
M, 2M, 3M, ...
4
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
1

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
sum = N * ( (first term + last term) / 2)
61

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
sum = N * ( (first term + last term) / 2)
64

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
66

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
68

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2
sum = N * ( (first term + last term) / 2)
71

N = B / M - (A - 1)/ M
7_______29_______73

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2
sum = N * ( (first term + last term) / 2)
76

N = B / M - (A - 1)/ M
7_______29_______78

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
80

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4 // C++ program to find the sum of numbers45
M, 2M, 3M, ...
79// C++ program to find the sum of numbers47

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
85

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9 // C++ program to find the sum of numbers53// C++ program to find the sum of numbers54using6

42
1

// divisible by M in the given range7

42
2

M, 2M, 3M, ...
28 #include <bits/stdc++.h>0
M, 2M, 3M, ...
30
M, 2M, 3M, ...
31

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
2

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
95

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
42
9

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
4
M, 2M, 3M, ...
39
M, 2M, 3M, ...
40
M, 2M, 3M, ...
41
M, 2M, 3M, ...
42
M, 2M, 3M, ...
43
M, 2M, 3M, ...
44using6

// divisible by M in the given range7

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____687_______4

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3// C++ program to find the sum of numbers81

// divisible by M in the given range7

42
1

42
1

 

// C++ program to find the sum of numbers85

Python3




// C++ program to find the sum of numbers86

M, 2M, 3M, ...
57

 

// C++ program to find the sum of numbers88

// C++ program to find the sum of numbers89

// C++ program to find the sum of numbers90

M, 2M, 3M, ...
60 // C++ program to find the sum of numbers92

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____687_______95

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3// C++ program to find the sum of numbers97

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3// C++ program to find the sum of numbers99_______0_______66 // divisible by M in the given range01
M, 2M, 3M, ...
88 // divisible by M in the given range03

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____688_______05

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____688_______07

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2 // divisible by M in the given range10
M, 2M, 3M, ...
66
M, 2M, 3M, ...
66 using5
M, 2M, 3M, ...
80

N = B / M - (A - 1)/ M
7_______29_______9 // divisible by M in the given range01

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
93
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
10

N = B / M - (A - 1)/ M
7_______688_______22

N = B / M - (A - 1)/ M
7_______688_______24

N = B / M - (A - 1)/ M
7_______688_______26

N = B / M - (A - 1)/ M
7_______29_______9 // divisible by M in the given range01// divisible by M in the given range30 // C++ program to find the sum of numbers99

 

// divisible by M in the given range32

// divisible by M in the given range33

// C++ program to find the sum of numbers90

M, 2M, 3M, ...
60 // divisible by M in the given range36

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____687_______95

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3// C++ program to find the sum of numbers97

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3// C++ program to find the sum of numbers99
M, 2M, 3M, ...
66 // divisible by M in the given range45
M, 2M, 3M, ...
78
N = B / M - (A - 1)/ M
73
M, 2M, 3M, ...
88 // divisible by M in the given range03

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____688_______05

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3____688_______07

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2 // divisible by M in the given range10
M, 2M, 3M, ...
66
M, 2M, 3M, ...
66 using5
M, 2M, 3M, ...
80

N = B / M - (A - 1)/ M
7_______29_______9 // divisible by M in the given range01

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
N = B / M - (A - 1)/ M
93
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
10

N = B / M - (A - 1)/ M
7_______688_______22

N = B / M - (A - 1)/ M
7_______688_______24

N = B / M - (A - 1)/ M
7_______688_______26

N = B / M - (A - 1)/ M
7_______29_______9 // divisible by M in the given range01
M, 2M, 3M, ...
78 // divisible by M in the given range03// divisible by M in the given range30 // C++ program to find the sum of numbers99

 

M, 2M, 3M, ...
58

M, 2M, 3M, ...
57

M, 2M, 3M, ...
60
M, 2M, 3M, ...
61

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
63

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
M, 2M, 3M, ...
65
M, 2M, 3M, ...
66 using5

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3// divisible by M in the given range92
M, 2M, 3M, ...
66 // divisible by M in the given range94

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3// divisible by M in the given range96
M, 2M, 3M, ...
66 // divisible by M in the given range98

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3#include <bits/stdc++.h>00

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3#include <bits/stdc++.h>02

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2 #include <bits/stdc++.h>05

N = B / M - (A - 1)/ M
7_______688_______92
M, 2M, 3M, ...
78
M, 2M, 3M, ...
66
M, 2M, 3M, ...
89

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
2 #include <bits/stdc++.h>13

N = B / M - (A - 1)/ M
7_______688_______92____688_______30
M, 2M, 3M, ...
66
M, 2M, 3M, ...
89

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3#include <bits/stdc++.h>20

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3#include <bits/stdc++.h>22
M, 2M, 3M, ...
66 #include <bits/stdc++.h>24#include <bits/stdc++.h>25#include <bits/stdc++.h>25
K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
1// divisible by M in the given range30 #include <bits/stdc++.h>29// divisible by M in the given range30
M, 2M, 3M, ...
79
M, 2M, 3M, ...
16#include <bits/stdc++.h>25#include <bits/stdc++.h>25
M, 2M, 3M, ...
89

 

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3#include <bits/stdc++.h>37

K, (K + M), (K + 2M), ------  (K + (N - 1)*M )
where N is the number of elements in the series. 
3
sum = N * ( (first term + last term) / 2)
9 #include <bits/stdc++.h>22#include <bits/stdc++.h>41 #include <bits/stdc++.h>42
M, 2M, 3M, ...
78 #include <bits/stdc++.h>44#include <bits/stdc++.h>25#include <bits/stdc++.h>25 // C++ program to find the sum of numbers54

Tổng của số chia hết cho 3 là bao nhiêu?

Theo quy tắc chia hết cho 3, một số được gọi là chia hết cho 3 nếu tổng các chữ số của số đó chia hết cho 3. For example, the number 495 is completely divisible by 3. The sum of all digits are 4 + 9 + 5 = 18 and 18 is divisible by 3.

Làm cách nào để kiểm tra xem một số có chia hết cho 3 và 5 trong C không?

printf("Số chia hết cho 3 và 5 trong khoảng từ 0 đến %d
là. \n", số);
for (i = 1; i <= num; i++){
nếu (i % 3 == 0 && i % 5 == 0){
printf("%d ", i);

Tổng tất cả các số chia hết cho 3 từ 1 đến 100 là bao nhiêu?

Giải pháp. Các số tự nhiên từ 1 đến 100 chia hết cho 3 là 3,6,9,…,99. Trình tự nằm trong A. P. Tổng tất cả các số tự nhiên từ 1 đến 100 chia hết cho 3 là 1683 .

Có bao nhiêu số chia hết cho 3?

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69 . Có 33 số có 2 chữ số chia hết cho 3.