Ah, OK, nevermind, I think I see it using the binomial formula on the term, giving a sum where one can deduce the stated property by factorization (the 1 and the first term in the series cancel).
I want to know whether there is an easy way to see how fast
goes to zero as a function of .
I already know (thanks Maple!) that for the function goes slower than , i.e.
(and for the limit is 1). But is there a clear and easy way to see this? I can't even do the limit by hand because it seems to require an infinite number of applications of L'hopitals rule...
Note: Obviously the case is easy since I can substitute and the thing goes to a constant .. but what about the cases when it really goes to zero? Obviously a=2 is special.
Thanks in advance.