Let be a real parameter and set for

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

Problem

Let

r>0

be a real parameter and set

a_n=r^{\,\ln n}

for

n\ge 1

. Determine all values of

r

such that the series

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

diverges by the

n

th term test.