(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a power series for the function, centered at c, and determine the interval of convergence.

2. Relevant equations

g(x) = 2 / (1-x^2) , c=0

3. The attempt at a solution

2 / (1+x)(1-x) = 1/(1+x) + 1/(1-x)

1/(1-(-x)) => Sum [(-1)^n (x^n)], n=0 to infinity. Converges when abs(x) < 1, (-1,1)

1/(1-x) => Sum x^n, n=0 to infinity. Converges when abs(x) < 1, (-1,1)

So, 2/(1-x^2) = Sum[(-1)^n + 1]x^n, n=0 to infinity.

OK, here's the part that is probably SO simple, but I'm just not seeing it. The book shows the series above, Sum[(-1)^n + 1]x^n, n=0 to infinity is then equal to:

Sum 2x^(2n), n=0 to infinity.

How do you do that last simplification? Sorry for such a simple question, but I'm stuck. :)

Also, the book has the interval of convergence for the series as abs(x^2)<1 or (1,1), which I'm pretty sure is just a typo. It should be (-1,1), right?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Stuck At the Last Step Simplifying A Series

**Physics Forums | Science Articles, Homework Help, Discussion**