For what values of will both series and converge?

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

Problem

For what values of

p

will both series

\sum_{n=1}^{\infty}\frac{1}{n^{2p}}

and

\sum_{n=1}^{\infty}\left(\frac{p}{2}\right)^n

converge?