Consider two positive-term series and

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

Problem

Consider two positive-term series

\sum a_n

and

\sum b_n

. Which of the following sets of conditions is sufficient to guarantee that

\sum_{n=1}^{\infty} a_n

converges? (a)

0 \le b_n \le a_n

for all

n

and

\sum b_n

converges. (b)

0 \le a_n \le b_n

for all

n

and

\sum b_n

converges. (c)

a_n \le b_n

for all

n

and

\sum b_n

converges (no restriction on signs). (d)

0 \le a_n \le b_n

for all

n

and

\sum b_n

diverges.