Find the sum of a mathematical series - c

Question

Write a program in C to find the sum of the series [ 1-X^2/2!+X^4/4!- .........]
Test Data:
Input the Value of x :2
Input the number of terms : 5
Expected Output:
the sum = -0.415873
Number of terms = 5
Here is the code I wrote, no compilation error, I just wasnt getting the answer right:
#include <stdio.h>
#include <math.h>
int main()
{
float sum=0;
float ans;
int c, y, fac=1;
int a,i, x=2;
float z;
for (i = 1; i<=2; i++)
{
a= 2*i;
y = pow(2,a);
for (c = 1; c<=a; c++)
{
fac= fac*c;
}
z = (float) y/fac;
if (i%2 == 0) {
sum = sum + z;
}
else{
sum = sum - z;
}
}
ans = 1 + sum;
printf("The answer is %f" , ans);
return 0;
}

Answer 1

You didn't used number of terms.
You didn't set fac to 1 to the end of the for.
y is equal to pow(x,a) not pow(2,a).
Int can store numbers between -2,147,483,648 and 2,147,483,647, so I recommend to use long long (-9,223,372,036,854,775,808 to 9,223,372,036,854,775,807). And also, double instead of float. You can take a look here for more details: https://learn.microsoft.com/en-us/cpp/cpp/data-type-ranges?view=msvc-160.
Here is the code:
#include <stdio.h>
#include <math.h>
int main()
{
double sum=0;
double ans;
long long c, y, fac=1;
long long a,i, x=2, numberOfTerms = 5;
float z;
for (i = 1; i<= numberOfTerms; i++)
{
a= 2*i;
y = pow(x,a);
for (c = 1; c<=a; c++)
{
fac= fac*c;
}
z = (double) y/fac;
if (i%2 == 0) {
sum = sum + z;
}
else{
sum = sum - z;
}
fac = 1;
}
ans = 1 + sum;
printf("The answer is %f" , ans);
return 0;
}

Answer 2

Try to use functions.
If you do not have to, do not use float. Use double for floating point calculations.
Your code does not reflect the formula at all.
double fact(unsigned n)
{
double result = 1.0;
for(unsigned x = 1; x <= n; x++)
result *= x;
return result;
}
double series(double x, unsigned nterms)
{
double result = 1;
for(unsigned term = 1; term <= nterms; term++)
{
result += (1.0 - ((term & 1) << 1)) * pow(x, (double)term * 2.0) / fact(term * 2);
}
return result;
}
int main(void)
{
for(unsigned nterms = 2; nterms < 20; nterms++)
{
printf("nterms = %2u series(4) = %.32f\n", nterms, series(4.0, nterms));
}
}
https://godbolt.org/z/8c3xM4