# How do you find a power series representation for #x/(1-x^2)# and what is the radius of convergence?

##### 1 Answer

Oct 24, 2015

Use the Maclaurin series for

#x/(1-x^2) = sum_(n=0)^oo x^(2n+1)#

with radius of convergence

#### Explanation:

The Maclaurin series for

since

Substitute

#1/(1-x^2) = sum_(n=0)^oo (x^2)^n = sum_(n=0)^oo x^(2n)#

Multiply by

#x/(1-x^2) = x sum_(n=0)^oo x^(2n) = sum_(n=0)^oo x^(2n+1)#

This is a geometric series with common ratio