## Two diverging series combined into a convergent series

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

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