C Program to find exponent Power Series

//C Program to find exponent Power 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
 
Explanation
A program to evaluate the power series
           x2      x3            xn
ex  =  1 + x + ---  +  --- + ..... + ---- , 0 &lt; x &lt; 1
                2!      3!            n!
It uses if……else to test the accuracy.
The power series contains the recurrence relationship of the type
        Tn   =  Tn-1  (---)   for n &gt; 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