Define and consider

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

Problem

Define

b_n = \dfrac{e^{1/n}-1}{1/n}

and consider

\displaystyle\sum_{n=1}^{\infty} b_n

. Which of the following is true? (a) The series converges because

\displaystyle\lim_{n\to\infty} b_n = 0

. (b) The series diverges because

\displaystyle\lim_{n\to\infty} b_n = 1

. (c) The series converges because

b_n \sim 1/n^{2}

for large

n

, a

p

-series with

p>1

. (d) The series converges because

\displaystyle\lim_{n\to\infty} b_n = 1