how does sigma work?

Question

I am having trouble understanding how the recursion in following code works. So I do understand that main prints the user input. Then the function sigma will print + and a decrementation of m until it reaches 0.

When it reaches 0 it will print = and the variable answer. What I do not understand is how return calculates the numbers together. Could anybody please explain how the return is doing this?

#include <cs50.h>
#include <stdio.h>

int sigma(int m)
{
    printf("%i", m);
    if (m == 0)
    {
        printf("=");
        return 0;
    }
    else
    {
        printf("+");
        return (m + sigma(m - 1));
    }
}

int main(void)
{
    int n = GetInt();
    int answer = sigma(n);
    printf("%i\n", answer);
}

Answer 1

Unroll sigma (5) and see what you get ..

sigma (5) = 5 + sigma (4)
      = 5 + (4 + sigma (3))
      = 5 + (4 + (3 + sigma (2)))
      = 5 + (4 + (3 + (2 + sigma (1))))
      = 5 + (4 + (3 + (2 + (1 + sigma (0)))))
      = 5 + (4 + (3 + (2 + (1 + 0))))
      = 5 + (4 + (3 + (2 + 1)))
      = 5 + (4 + (3 + 3))
      = 5 + (4 + 6)
      = 5 + 10
      = 15

Note that calling sigma with a negative parameter will break your program.