Let and for every integer

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

Problem

Let

a_n>0

and

b_n>0

for every integer

n\ge 1

. If

\displaystyle \lim_{n\to\infty}\frac{a_n}{b_n}=5

, what can you conclude about the convergence of the two series

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

and

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