Hey folks.

I still havent got my head round the idea of a series expansion and am stuck on the questions in my homework regard series expansion.

1) What is the series expansion of

and it's radius of conversion?

There is a an x-formula in my textbook which reads

. First of all I don't exactly understand where it has come from (the explanation isn't clear) and secondly, can I just plug in my "x" is into the formula?

I know the Radius of Convergence is when the function doesn't make sense so for the question the ROC is infinity i.e. it always makes sense?