Possible Duplicate:
Contest problem about convergent series
Let ${p}_{n}\in \mathbb{R} $ be positive for every $n$ and $\sum_{n=1}^{∞}\cfrac{1}{{p}_{n}}$ converges,
How do I show that $\sum_{n=1}^{∞}{p}_{n}\cfrac{{n}^{2}}{{({p}_{1}+{p}_{2}+\dotso+{p}_{n})}^{2}}$ converges?