Question

Find a power series representation for 1/(x+2)

Answer 1

\[\frac {1}{x+2} = \frac {1}{1 - (-1 - x)}\]\[\sum_{n= 0}^{\infty} (-1 - x)^n = \sum_{n= 0}^{\infty} (-1)^n (1 + x)^n\]

Answer 2

Is the way to approach these problems simply to relate them back to the geometric series

\[\sum_{n=0}^{\infty} x^n = 1/(1-x)\]

Answer 3

Yup, that's the easiest way to do them, unless you want to bang it out and do it like a Taylor series.

Answer 4

Awesome, thanks :D