Convergence and Divergence Question 7

If the series \(\displaystyle \sum_{n=1}^\infty a_n \) converges and \(a_n \gt 0 \) for all \(n\), which of the following must be true?

\( \displaystyle \lim\limits_{n\to\infty} \left| \frac{a_{n+1}}{a_n} \right| = 0 \)

\( \displaystyle \sum_{n=1}^\infty a_n=0 \)

\( \displaystyle \sum_{n=1}^\infty na_n\) diverges.

\( \displaystyle \sum_{n=1}^\infty \frac{a_n}{n}\) converges.