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
C Program for Exponent Series :
#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 = %f\n", 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
