Infinite Sequences and Series · Superchallenge problem

Let $H_n=1+\dfrac12+\cdots+\dfrac1n$. Given that $\displaystyle\sum_{k=1}^{\infty}\frac1{k^2}=\frac{\pi^2}{6}$, find the exact value of $\displaystyle\sum_{n=1}^{\infty}\frac{H_n}{n(n+1)}$.