# Thread: differentiation and power series representation

1. ## differentiation and power series representation

this was a very long problem. was confusing to jump back and forth, need help breaking this one down please.

heres the questions and the problem:

use differentiation to find a power series representation for f(x) 1/(1+x)^2

what is the radius of convergence?

b.) use part(a) to find a power series for f(x) = 1/(1+x)^3

c.) use part (b) to find a power series for f(x) = x^2/(1+x)^3

2. Originally Posted by rcmango
this was a very long problem. was confusing to jump back and forth, need help breaking this one down please.

heres the questions and the problem:

use differentiation to find a power series representation for f(x) 1/(1+x)^2

what is the radius of convergence?

b.) use part(a) to find a power series for f(x) = 1/(1+x)^3

c.) use part (b) to find a power series for f(x) = x^2/(1+x)^3
Note that 1/(1 + x)^2 = - d/dx [1/(1 + x)]

and you know the power series representation as TPH calculated it for you here

turn his answer into a single expression (it would be SUM{n goes from 0 to infinity} (-1)^n *x^n) and differentiate that expression, and add a minus sign in front and you will have the answer for part (a). the other parts are similar.

3. ya, theres alot going on in that problem. thanks for the help.