- #1

- 1,456

- 44

## Homework Statement

Show that ##\displaystyle \frac{1}{1+x^2} = \frac{1}{x^2} - \frac{1}{x^4} + \frac{1}{x^6} - \frac{1}{x^8} + \cdots##

## Homework Equations

## The Attempt at a Solution

I know that the power series expansion of ##\displaystyle \frac{1}{1+x^2}## about ##x=0## is ##1-x^2 + x^4 - x^6 + \cdots##, but I don't see how this can translate into the expressions as above.