How to prove this series converges to an irrational?

Question

I think his problem is very interesting

Let k>=2 be an integer and let p be a polynomial of degree >=2 with integer coefficients such that the coefficient of the leading term is positive. Prove that Sum (k=1, oo) 1/(k^p(n))converges to an irrational number.

Answer 1

Definitely interesting... ill work on it for a bit... ^o) definitely will keep my eye on this

EDIT

So essentiall you want ust to prove that the riemann zeta is irrational for all integers (since you placed no real restrictions on the polynomial other than 'large' enough to converge).

Its known for even integers and unknown for most odd.

Is this a cruel joke?

Answer 2

Wow i thought i was good at maths and that goes right over my head!!!