C Program for Exponent Series

Program :
A program to evaluate the power series

           x2      x3            xn
ex  =  1 + x + ---  +  --- + ..... + ---- , 0 < x < 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 > 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

---

#include<stdio.h>
#define ACCURACY 0.0001                                     

main()
{
 int n, count;
 float x, term, sum;

 printf("Enter 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("Terms = %d Sum = %fn", count, sum);
 }

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