Let be a real constant

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

Problem

Let

p

be a real constant. For the series

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

for which values of

p

does the

n

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

p<1

(b)

p\le 0

p

(d)

p<0

only