Suppose $a_n\geq0$ and $\sum a_n$ is convergent. Show that $ \sum 1/(n^2\cdot a_n)$ is divergent. I haven't been able to get any result from any of my approaches (which include the general tests for positive series). However if I were to create $\sum b_n$ such that the terms are in the same order as in $\sum a_n$ except the terms for which $a_n=0$ have been omitted, then of course I would be able to solve it. But would this approach be correct.
I was also wondering whether some result related to p test could be used.
Or, if you have a better approach please do share it