1. ## Manipulating power series

Find a power series representation of the function:

$f(x) = \frac{8}{1-x^7}$

and determine the interval of convergence.

Here is my work:

$8 \sum^{\infty}_{n=0} (x^7)^n$

$= \sum^{\infty}_{n=0} 8x^{7n}$

Ok, I found my interval of convergence:

-1 < x <1

But to test each end point, where do I plug those into? Into the series $(x^7)^n$ ?

2. the end points are x=1 and x=-1, so you must change x by those values in the series and determine its convergence