Let be a real number

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

Problem

Let

p

be a real number. Consider the series

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

. For which values of

p

must this series diverge? (a)

|p|>1

(b)

|p|\ge 1

(c)

|p|>1\,\text{ or }\,p=1

(d)

p=1