Write C program to find Exponent Power Series

Program :

A program to evaluate the power series

             x2   x3            xn
ex = 1 + x + --- + --- + ..... + ---- 
             2!     3!            n!
, 0 < x < 1

It uses if……else to test the accuracy.

The power series contains the recurrence relationship of the type

Tn = Tn-1 (---) for n > 1

T1 = x for n = 1

T0 = 1

If Tn-1 (usually known as previous term) is known, then Tn (known as present term) can be easily found by
multiplying the previous term by x/n. Then

ex = T0 + T1 + T2 + ...... + Tn = sum

C Program for Exponent Series :

#include <stdio.h>
#define ACCURACY 0.0001
 
int main() {
   int n, count;
   float x, term, sum;
 
   printf("\nEnter value of x :");
   scanf("%f", &x);
 
   n = term = sum = count = 1;
 
   while (n <= 100) {
      term = term * x / n;
      sum = sum + term;
      count = count + 1;
 
      if (term < ACCURACY)
         n = 999;
      else
         n = n + 1;
   }
 
   printf("\nTerms = %d Sum = %f", count, sum);
   return 0;
}

Output :

Enter value of x:0
Terms = 2 Sum = 1.000000
 
Enter value of x:0.1
Terms = 5 Sum = 1.105171
 
Enter value of x:0.5
Terms = 7 Sum = 1.648720
 
Enter value of x:0.75
Terms = 8 Sum = 2.116997
 
Enter value of x:0.99
Terms = 9 Sum = 2.691232
 
Enter value of x:1
Terms = 9 Sum = 2.718279