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?
2) Use the fact that to calculate a simpler derivation of this result.
Im not at all sure where to start...something to do with De Moivre's theorem I beleive but I've never really understood it? Could you point me in the right direction or more?
Thanks a lot people