Thread: 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

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.

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