if Sn is the summation of partial sums from 1 to infinity of (log n)^-logn, prove whether Sn converges or diverges.

It gives a hint of using the 2^m test which states that if Am is a nonincreasing function with limit 0 then the Summation of An from 1 to infinityconverges if and only if the series of the summation of partial sums 2^m*A(2^m) from m=0 to m=infinity