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# 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
```

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