According to worlpramalpha the sum diverges with comparison test...
then what do we compare this sum with, and how to deal with this log function...
by making a few graphs one can see that for example is eventually smaller then this log-function,
which indeed suggests the sum diverges...
Then is an argument by comparing derivatives enough?
Like and
implying the derivative of is eventually smaller then that of the log-function..bla bla
sufficient? More clever ideas ? (a)