Question

can anyone help me how to prove Σ1/n^logn, Σa^logn and Σ1/(logn)^logn are converge or not?

Answer 1

Looking first at \( Σ \ 1/n^{\ln n} \), this about what you know: \( \Sigma 1/n \) does not converge but Σ1/n^2 does.

Does lnn get larger than 2 for sufficiently large n? Can you therefore compare it with a convergent series therefore?

Answer 2

I see. Tq JamesJ