Which of the following statements is NOT required for the convergence of an…

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

Problem

Which of the following statements is NOT required for the convergence of an alternating series of the form

\sum_{n=1}^{\infty} (-1)^{n} a_n

? (a)

a_{n+1}\le a_n

for all sufficiently large

n

. (b)

a_n>0

for all sufficiently large

n

. (c)

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

converges. (d)

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