the the sum (using the integral test) from k=1 to infinity of (lnk)^2/k
I said divergent because the interval goes to infinity
is this correct?
integral of dx(ln x)^2 /x from 1 to oo is:
(1/3)(ln oo)^3 - (1/3) (ln 1)^3
although ln 1 is politely zero, ln oo is not finite so the series which is underestimated by the integral is not convergent