C program to calculate sum of series using predefined function

Problem

The program to calculate the sum of the following expression

Sum=1-n^2/2!+n^4/4!-n^6/6!+n^8/8!-n^10/10!

User has to enter the value of n at runtime to calculate the sum of the series by using the predefined function power present in math.h library function.

Solution

It is explained below how to calculate sum of series using predefined function.

Algorithm

Refer an algorithm given below to calculate sum of series by using the predefined function.

Step 1 − Read the num value

Step 2 − Initialize fact = 1, sum = 1 and n =5

Step 3 − for i= 1 to n

   a. compute fact= fact*i
   b. if i %2 = 0
   c. then if i=2 or i=10 or i=6
   d. then sum+= -pow(num,i)/fact
   e. else sum+=pow(num,i)/fact
   4. print sum

Example

Following is the C program to calculate sum of series by using the predefined function −

#include<stdio.h>
#include<conio.h>
#include<math.h>
void main(){
   int i,n=5,num;
   long int fact=1;
   float sum=1;
   printf("Enter the n value:");
   scanf("%d", &num);
   for(i=1;i<=n;i++){
      fact=fact*i;
      if(i%2==0){
         if(i==2|i==10|i==6)
            sum+= -pow(num,i)/fact;
         else
         sum+=pow(num,i)/fact;
      }
   }
   printf("sum is %f", sum);
}

Output

When the above program is executed, it produces the following result −

Enter the n value:10
sum is 367.666656