Question

Represent the following as a power series

Answer 1

\[\frac{ 1+x }{ 1-x }\] Also Find the interval of convergence and Radii

Answer 2

WOW can't believe you're still here! Dedication! Thanks man!

Answer 3

It's not too difficult to show that \(\dfrac{1+x}{1-x} = -1 + \dfrac{2}{1-x}\) (use long division).

Now recall that \(\large \displaystyle \frac{1}{1-x}=\sum\limits_{n=0}^{\infty} x^n\) given that \(\large |x|<1\) (i.e. this is a geometric series).

With this, what is the series representation?

(with regards to dedication, it's more or less that I was busy doing other stuff in the midst of writing this up..haha)

Answer 4

;) So that ends up being...