Explain why the series must converge if for all and for all sufficiently large

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

Problem

Explain why the series

\sum_{n=1}^{\infty} a_n

must converge if

a_n \ge 0

for all

n

and

a_n \le \dfrac{5}{n^{3}}

for all sufficiently large

n

. State your reasoning in one or two sentences.