Divergence of a Certain series

From: ptk (ptk_at_nospam4me.net)
Date: 01/16/05 

Date: Sun, 16 Jan 2005 02:04:05 GMT

Let H(n) = 1 + (1/2) + (1/3) + ... + (1/n) = sum of the first n terms
of the harmonic series. Note that

\lim_{n \to \infty} \frac{H(n)}{n} = 0 and \sum_{n = 1}^\infty
{\frac{H(n)}{n}} diverges.

Question: Does \sum_{n = 1}^\infty {(\frac{H(n)}{n})^2} converge?
(Proof requested)