Find and state whether the series whose th term is converges or diverges.

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

Problem

Find

\displaystyle\lim_{n\to\infty} \dfrac{\ln(n+1)-\ln n}{1/n}

and state whether the series whose

n

th term is

a_n=\dfrac{\ln(n+1)-\ln n}{1/n}

converges or diverges.