Consider the series _ n=1 ^ n^ p n^ p +1

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the series

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

where

p

is a real parameter. For which values of

p

does the

n

th–term test indicate that the series diverges? (a)

p\ge 0

(b)

p>0

only (c) All real numbers

p

(d)

p<0

only