C中的总和，来自两个数字

Question

Im creating a simple program in C that user insert a number, for example 5 and the program sums until 5, 0+1+2+3+4. Im using this formula

int sum_naturals(int n){
    return (n-1)*n/2;
}

But now i want a formula that can sum from 2 different numbers, like user inserts number 5 and 9 and the program will do 5+6+7+8+9.

Can someone have ideia how can resolve this? Thanks

Answer 1

You can reuse your function

int sum(int a, int b) {
  return sum_naturals(b) - sum_naturals(a-1)
}

Of course you have to add some validation.

Answer 2

Why not this?

 int sum_2_naturals(int n, int m){
    return (sum_naturals(m) - sum_naturals(n))
}

Answer 3

But now i want a formula that can sum from 2 different numbers,

To find the sum of a certain number of terms of an arithmetic sequence:

#include <stdio.h>

static int sum_naturals(int a, int b)
{
    return ((b - a + 1) * (a + b)) / 2;
}

int main(void)
{
    printf("%d\n", sum_naturals(5, 9));
    return 0;
}

Output:

35

More info

Answer 4

Looks like a simple task, but since you still have problems understanding it, why don't you 'define' your functions first - before 'coding' them.

S ( n ) = 0 + 1 + 2 + ... + n -1 = n ( n -1)/2

F ( k , n ) = k + k +1 + ... + n -1 + n = -(0 + 1 + ... + k -1) + (0 + 1 + ... + k -1) + k + k +1 + ... + n -1 + n = - S ( k ) + S ( n ) + n = S ( n +1) - S ( k )

Of course, need to assume that k <= n etc.

I guess the reason of all confusion is that you defined your basic function to sum from 0 to n -1, instead of 1 to n .