Question: Determine whether the series is convergent or divergent, and if it is possible, find the sum.

At this point in my class, we only know geometric series, the divergence test, and the p-series. So we cant use integral test, comparison test etc. My initial attempt was to use the divergence test. But I am having a hard time evaluating the limit. Thanks in advance.

p.s the sigma goes from n=1 to infinity.