C 数学求解和代码结果的程序差异

Question

I like to calculate the following formula using c programming. The formula is as follows:

I have written the c program based on this formula

#include<stdio.h>
#include<math.h>
int main(){
     int n,i;
     double sum=0;
     printf("Enter the value for n");
     scanf("%d",&n);
     for (i=0; i<=n; i++){

     sum = sum + 4*(pow(-1,i))/((2*i)+1);
     }
     printf("sum of the series: %lf",sum);
}
return 0;

I am sharing the result that I have got after run the program and the result I got while calculating the result mathematically.

As you can see from picture 1 if I try to calculate the sum for different value of n like 1, 4,13 the sum was 2.67, 3.339, 3.0702 respectively.

However, when I tried to calculate this formula mathematically I got some different result.

Mathematically I got

n= 1 ans: 3.2

n=4 ans: 0.96825

Can anyone please guide what I am missing in code?

Thank you.

Answer 1

In 2nd iteration of your manual calculation, 2x1 + 1 = 3 but you're taking it as 5