Does 1/ nlognloglogn converge or diverge?
I am trying to show this with cauchy Condensation using 2^k in the new series. I have
reduced it to
(1/log2) E 1/ n(logn+loglog2)
where E is the sum from n=3 to infinity. I think it diverges, and am trying to show that this expression is larger than
E 1/ n(logn) which I have seen diverges, but the extra n in the denominator is messing me up. Can someone show me how to bound this, or if I am going about this the wrong way?