Hmmm...I'm afraid clearly Drexel has misread Tonio's solution: since the positive infinite series \(\displaystyle \sum^\infty_{n=1}a_n\) converges then \(\displaystyle a_n\xrightarrow [n\to\infty]{}0\Longrightarrow \frac{1}{a_n}\xrightarrow [n\to\infty]{}\infty\) .

Hmmm...I'm afraid clearly Drexel has misread Tonio's solution: since the positive infinite series \(\displaystyle \sum^\infty_{n=1}a_n\) converges then \(\displaystyle a_n\xrightarrow [n\to\infty]{}0\Longrightarrow \frac{1}{a_n}\xrightarrow [n\to\infty]{}\infty\) .