The Cauchy Criterion of a series is as follow:
Theorem: Let $a_n$ be a real sequence. Then the infinite series $\sum_{k=1}^{+\infty}{a_k}$ converges if only if for every $\varepsilon > 0$ there is an $N \in \mathbb{N}$ such that $m > n > N$ implies $$ \left| \sum_{k=n+1}^{m}{a_k} \right| < \varepsilon . $$
From this result, how to demonstrate the following corollary?
Corollary: Let $a_n$ be a real sequence. Then the infinite series $\sum_{k=1}^{+\infty}{a_k}$ converges if only if for every $\varepsilon > 0$ there is an $N \in \mathbb{N}$ such that $n > N$ implies $$ \left| \sum_{k=n+1}^{+\infty}{a_k} \right| < \varepsilon . $$