Possible Duplicate:
Slowing down divergence 2
If $\{a_n\}$ and $\{b_n\}$ are two increasing sequences of positive numbers such that both $\displaystyle\sum_{n=1}^{\infty} \frac{1}{a_n}$ and $\displaystyle\sum_{n=1}^{\infty} \frac{1}{b_n}$ are divergent. Then is it true that the series $\displaystyle\sum_{n=1}^{\infty} \frac{1}{a_n+b_n}$ is also divergent?
I think the answer is no, but I cannot come up with an appropriate example. Thanks!