Question: Say that $\sum a_n$ converges and $a_n$ does not equal 0 for all natural numbers.
Prove: $\sum 1/a_n$ diverges.
My understanding: I see that $1/a_n$ is the reciprocal of $a_n$. I have done many examples with numbers that prove this theorem, but I am not sure how to really prove this without testing numbers with convergence/divergence tests. Would I use the comparison theorem test here?