Problem 28
By Supreme2023-03-15
Problem Statement :
Write a program to evaluate the series sum=1-x+x^2/2!-x^3/3!+x^4/4!......-x^9/9!
Code:
#include <stdio.h>
#include <math.h>
float series (float x, int n);
int main(){
printf("\t\tEvaluation Of Given Series");
printf("\n\t1 - x + x^2/2! - x^3/3! + x^4/4!......- x^9/9!");
printf("\n============================================================\n");
float x;
int n=9;
printf("\nEnter The Value Of X : ");
scanf("%f",&x);
float answer = series (x,n);
printf("\nAnswer = %.4f ",answer);
return 0;
}
float series(float x,int n){
float sum=1,sign=1,fact,j,y=1,term;
int i;
for(i=1;i<=n;i++){
fact=1;
for(j=1;j<=y;j++){
fact *= j;
}
sign = pow((-1),i);
term = sign*pow(x,y)/fact;
sum += term;
y++;
}
return sum;
}
Description :
- This program evaluates the given series: 1 - x + x^2/2! - x^3/3! + x^4/4! - x^5/5! + x^6/6! - x^7/7! + x^8/8! - x^9/9!
- The program includes two libraries: stdio.h and math.h.
- The main function starts by printing the series to be evaluated.
- It prompts the user to input the value of x.
- It initializes the number of terms in the series (n) to 9.
- It calls the series function and passes the values of x and n to it.
- The series function takes two arguments: x and n, and returns the sum of the series.
- Inside the series function, it initializes the first term of the series to 1.
- It declares some variables including sign, fact, j, y, and term.
- It starts a loop from i=1 to n.
- It initializes the factorial (fact) to 1.
- It calculates the factorial of y by starting another loop from j=1 to y.
- It multiplies the factorial by j for each iteration.
- It calculates the sign of the term based on the current iteration of i.
- It calculates the term by raising x to the power of y, multiplying by the sign, and dividing by the factorial.
- It adds the term to the sum.
- It increments y by 1 for the next iteration.
- After the loop is completed, the function returns the sum of the series.
- Finally, the main function prints the result returned by the series function.
Output Image:
