In passing let me mention that a formula for the sum of k to the power p
(for k=1 to n-1) using Bernoulli numbers is included in G. Carr, Formulas
and Theorems, paragraph 2939 (the book Ramanujan loved, and reprinted by
Chelsea Publications). The reason I mention is because Carr has a misprint
there: the n on line 4 of paragraph 2939 should be a p.
Michael Lambrou
Department of Mathematics
University of Crete
Iraklion 71409
Greece
e-mail: LAMBROU@TALOS.CC.UCH.GR