evaluate the series as many ways as possible
both methods given by Mathstud28 and Krizalid are good but they're not strong enough to handle the general form, i.e. evaluating: where is given.
note that the sum here starts from which is more usual than k = 2. evaluating is quite easy if you're familiar with gamma and beta functions. here's the solution: first observe that:
from here things are straightforward:
as a result, if you really want your sum to start from you will get: