Do the following series converge or diverge?

Sum(1/(k^(1/3)) k=0..infinity

Sum(1/(k*log(k)) k=2..infinity

What is the sum (exact form) of

Sum(k*p^(k-1)) k=0..infinity and |p|<1

^ is power to

* is multiplication

[Difficulty]

For the first two I tried the Ratio and Root test and found L=1 in

both cases. Also the divergence test is inconclusive. How do I

determine if the series converges or diverges?