C program to find the sum of factorials

I was trying to compute the sum of series which involves factorials.

The series is: 1 + 1/2! + 1/3! + 1/4! + ...

btw 3! = 1 x 2 x 3

4! = 1 x 2 x 3 x 4

...so on, it continues like this for every number

This is the code I've written to run the C program:

#include <stdio.h>

void main() {

    /* Any problems with the variables? */
        
    int i, lim, fact = 1;
    float sum = 0.0, term;
    
    printf("Enter the limit for the sum of series: ");
    scanf("%d", &lim);
    
    /* Any problems in the loop? */
    
    for (i = 1; i <= lim; i++) {
        fact *= i;
        term = 1 / fact;
        sum += fact; 
    }

    printf ("%f is the sum of the series\n", sum);
}

Is there any syntax error here that I just can't see or something, or is it a problem of the compiler. If so, I'm using gcc on ubuntu. Nevertheless, I'm not getting the correct output.

Solution

There are some mistakes in your code.

The first one, is very common when we start learning C

1 / fact must be replaced by 1.0f / fact

Why? Because in C, 1 / 2 is performed using integer arithmetic and returns 0. If you want to perform computation using floating numbers you must force at least one argument being a floating number, this can be done by 1.0/2, 1/2.0 or 1.0/2.0. The previous expressions will be evaluated using double floating number type (which is the C default type for floating number). If you want to use simple precision floating numbers, float, you can use 1.0f

the second one is certainly an inadvertent error:

sum += fact; must be replace by sum += term;

Here is a "working" code

#include <stdio.h>

void
main()
{
  /*Any problems with the variables ?*/

  int i, lim, fact = 1;
  float sum = 0.0, term;

  printf("Enter the limit for the sum of series: ");
  scanf("%d", &lim);

  /*Any problems in the loop ? */

  for (i = 1; i <= lim; i++)
  {
    fact *= i;
    term = 1. / fact; /* instead of 1/fact */
    sum += term;      /* instead of sum += fact */
  }

  printf("%f is the sum of the series\n", sum);
}

Enter the limit for the sum of series: 5

1.716667 is the sum of the series

There is a more subtle error. By instance, if you want lim = 50,

Enter the limit for the sum of series: 50

inf is the sum of the series

The reason is that 50! is way too big to be stored in an int.

The solution is to compute directly 1/i! using floating number (and not i! using int then 1/i!)

A modified program, that also uses double for an higher precision is :

#include <stdio.h>

void
main()
{
  /*Any problems with the variables ?*/

  int lim;
  double sum = 0.0, term = 1.0;

  printf("Enter the limit for the sum of series: ");
  scanf("%d", &lim);

  /*Any problems in the loop ? */

  for (int i = 1; i <= lim; i++)
  {
    term = term / i;
    sum += term;
  }

  printf("%f is the sum of the series\n", sum);
}

that now works, even when lim=50

Do not be discouraged by these mistakes. These are mistakes we all made when we learned C !

Expected result:

exp(1) = exp(0) + sum_{i=1}^\infty 1/i!

thus your expected result is exp(1)-exp(0) = 1.718281828459045....