For the family of series with real parameter

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

Problem

For the family of series

\displaystyle \sum_{n=1}^{\infty}\frac{n}{n^{p}+3}

with real parameter

p

, find all values of

p

for which the limit of the

n

th term alone guarantees that the series cannot converge.