Provide an explicit example of a series whose terms satisfy but the series diverges

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

Problem

Provide an explicit example of a series whose terms satisfy

\displaystyle \lim_{n\to\infty} a_n = 0

but the series diverges. State the series and name a commonly used test that can confirm its divergence (do not perform the test).