Originally Posted by

**nsievers**
Hello all,

My class went over power series representation a few days ago and I am having some trouble. Here is the problem I'm working on, and how I have tried to solve it:

"use differentiation to find a power series representation of f(x) = (2+x)^(-2)"

(2+x)^(-2) = d/dx (-1)/(2+x) = d/dx (-1/2)/(1-(-x/2))

d/dx (summation from n = 0 to infinity) (-1/2)(-x/2)^n

(summation from n = 1 to infinity) (n)(-1/2)(-x/2)^(n-1)

ANSWER: (summation from n = 0 to infinity) (n + 1)(-1/2)(-x/2)^n

Can someone please explain what it is that I am doing wrong?

## Bookmarks