Explain why the series must diverge if does not exist

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Explain why the series

\sum_{k=1}^{\infty} a_k

must diverge if

\lim_{n\to\infty} S_n

does not exist, where

S_n=\sum_{k=1}^{n} a_k