Question

Find a power series representative of the function and determine the interval of convergence.
\[f(x)=\frac{3}{1-x^4}\]

Answer 1

sorry it's the first problem in the section, can you give me a hint on where to start?

Answer 2

well I understand that I have to change it into the form
\[\sum\] somehow

Answer 3

\[\frac{1}{1-x^4}=\sum_{k=0}^{\infty}x^{4k}\]
how and why does the left side equal the right side?

Answer 4

I have access to the solutions, but don't quite understand them

Answer 5

I can figure out how to manipulate \[\frac{1}{1-x}= \sum_{n=0}^{\infty} x^n\]
to look like
\[\frac{1}{1-x^4}=\sum_{k=0}^{\infty}x^{4k}\] but I would prefer to understand how so