This is a question from a text book (Saff and Snider, Complex analysis for matemetics science and engineering).
Obtain the general formula for the laurent expansion of $$ f_n(z) = \frac{1}{(z-\alpha)^n}$$ $$(n = 1,2,...)$$ that is valid for $|z| > |\alpha|$
I have been scratching arround with geometric series and the formula $$\sum_{n=0}^\infty b^n = \frac{1}{1-b}$$ where $|b|<1$ but I can't seem to make progress. Acording to the solutions the answer is;
$$\sum_{j=n}^\infty \alpha^{j-n} \frac{(j-1)!}{(j-n)!(n-1)!} z^{-j}$$
(Also is this actualy difficult or am I just an idiot?)