6.3. Power Series

Let us write a program to evaluate the power series. The series looks like e**x =1+x+x**2/2! +x**3/3! +....+ x**n/n! where 0 < x < 1

#!/usr/bin/env python
x = float(raw_input("Enter the value of x: "))
n = term = num = 1
sum = 1.0
while n <= 100:
    term *= x / n
    sum += term
    n += 1
    if term < 0.0001:
        break
print "No of Times= %d and Sum= %f" % (n, sum)

The output

$ ./powerseries.py
Enter the value of x: 0
No of Times= 2 and Sum= 1.000000
$ ./powerseries.py
Enter the value of x: 0.1
No of Times= 5 and Sum= 1.105171
$ ./powerseries.py
Enter the value of x: 0.5
No of Times= 7 and Sum= 1.648720

In this program we introduced a new keyword called break. What break does is stop the innermost loop. In this example we are using break under the if statement

if term < 0.0001:
        break

This means if the value of term is less than 0.0001 then get out of the loop.