### Home > APCALC > Chapter 10 > Lesson 10.2.1 > Problem10-109

10-109.

Suppose $S = \displaystyle\sum _ { n = 1 } ^ { \infty } a _ { n }$ is a convergent series and $a_n ≠ 0$ for any $n$. Explain why the series $T = \displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 1 } { a _ { n } }$ must diverge.

$\lim\limits_{n\to\infty}a_n=0\text{, so }\lim\limits_{n\to\infty}\frac{1}{a_n}=?$