C program for calculating the value of e - c

Question

I was assigned a Hw that required me to calculate the value of e via using the series:
1 + 1/1! + 1/2! + ...1/n!
The value of e must be calculated until the value of n (entered by the user) is reached. Also, the value of 1/n! must be calculated until it's value is smaller than epsilon (also entered by the user).
I wrote the code, but there are some errors that compiler is telling me errors such as relational comparisons, use of ';' etc. Could anyone please help me fix the error. Thank you in advance.
Below is my code:
#include<stdio.h>
int factorial (int i)
{
if (i==0)
return 1;
else
return i*factorial(i-1);
}
int main(void) {
int i,n;
float e,ep;
printf("what is the value of epsilon: ");
scanf("%f",&ep);
printf("what is the value of n: ");
scanf("%d",&n);
for (i=1; i<=n, i++)
e= 1+1/factorial(i);
for(1/fatorial(i)<=ep)
printf("The value of e for the entered value of epsilon and n:%f",e);
return 0;
}

Answer 1

For more precision I would use double instead of float.
for (i=1; i<=n, i++)
e= 1+1/factorial(i);
This is wrong, you are not adding to e, you are assigning always the last
value of the series, which is always 0 (except for i = 1). So your e will
always be 1.
factorial is a function that returns an int. A int divided by an int is
an int and in C anything 1/x (for x > 1, x integer) is 0. You you to use
1.0 or cast at least one of the arguments to double (or float if you are
using floats):
double e = 1; // initializing e
for(i = 1; i <= n; ++i)
e += 1.0/factorial(i);
Also, the value of 1/n! must be calculated until it's value is smaller than epsilon, also entered by the user.
I don't understand what that means, if n is a fixed value given by the user,
what do you keep calculating? Is this really what the exercise says?
My interpretation would be: if by n steps |e_real - e_calculated| > epsilon,
keep incrementing n, otherwise stop. That would be
#include <stdio.h>
#include <math.h>
#include <stdint.h>
uint64_t factorial (uint64_t i)
{
if (i==0)
return 1;
else
return i*factorial(i-1);
}
int main(void)
{
int n;
double e = 1;
double epsilon;
printf("what is the value of epsilon: ");
scanf("%lf", &epsilon);
printf("what is the value of n: ");
scanf("%d",&n);
int i = 1;
while(1)
{
e += 1.0/factorial(i++);
if(i >= n && (fabs(e - M_E) < epsilon))
break;
}
printf("e: %.20lf, calculated e: %.20lf, error: %.20lf, steps: %d\n", M_E, e, fabs(e-M_E), i);
return 0;
}
Note: if you are using GCC, you have to compile it with the -lm option:
$ gcc e.c -oe -lm

Answer 2

You're not summing the series but actually set e to 1.
Because you set it to e + 1/factorial(n) but your factorial() returns an int which is very likely to be above 1, so the division is integral, and 1 divided by any greater number will give 0.
The last loop is very strange. Did you mean while rather than for? Note that factorial is mistyped. Moreover, no work is done in the loop's body other than printing the same message over and over.