Find examples of two series $\displaystyle \sum {a_n}$ and $\displaystyle \sum {b_n}$ both of which diverge but for which $\displaystyle \sum {min(a_n, b_n)}$ converges. Also $\displaystyle (a_n)$ and $\displaystyle (b_n)$ are positive and decreasing sequences.

I just cannot seem to find an example to make this true. Any help would be appreciated.