I'm trying to prove that if s is real and s>1 then
By letting I can then show that diverges (I hope).
I've tried all sorts of expressions for the left hand side of the inequality and don't seem to be able to get anywhere.
So the right side is bounded (presumably by pi^2/6) as s tends to 1. Also, zeta(1) is just the harmonic series (which diverges) and so does its logarithm. I'm fine with that.
So how does this show that the sum also diverges? Is there a theorem about the sum of two divergent series or something?