State the condition on the limit that guarantees convergence of the series under the…

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

Problem

State the condition on the limit

L=\displaystyle\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|

that guarantees convergence of the series

\sum a_n

under the ratio test.