[seqfan] Conjectured sum

[Vladimir Reshetnikov]

Hi,

Here is a conjecture:

sum(sum(4*(-1)^(i + 1)/(3*i^4), i = j .. inf), j = 1 .. inf) = zeta(3)

zeta(3) is the Apery's constant.

Can anybody prove of disprove it?

Thanks
Vladimir