If we know that $\sum_{n=1}^{\infty}a_n$ converges,
what (if anything) can be known about $\sum_{n=1}^{\infty}\frac{1}{a_n}$ ?
I understand that convergence means the summation adds up to a number so this is the statement I have come up with so far:
if the number $\sum_{n=1}^{\infty}a_n$ converges to is $< 0$ or $> 0$ then $\sum_{n=1}^{\infty}\frac{1}{a_n}$ converges also. otherwise if the number $\sum_{n=1}^{\infty}a_n$ converges to $= 0$, $\sum_{n=1}^{\infty}\frac{1}{a_n}$ does not converge.