2.

(a) Find all p ?: 0 such that the following series converges.

00 1 L k logP(k + 1)

k=l

(b) For each such p, prove that the partial sums of this series Sn and its value S satisfy n+ p -1( 1 )

Is - snl:S n(p _ 1) logP-l(n)

for all n ?: 2.