Let . Which statement best describes the convergence of…

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

Problem

Let

T=\displaystyle \sum_{n=1}^{\infty} (-1)^{n}\dfrac{4^{n}}{5^{n}+n^{2}}

. Which statement best describes the convergence of

T

? (a)

T

diverges because the terms do not approach

0

. (b)

T

converges conditionally but not absolutely. (c)

T

converges absolutely. (d)

T

diverges because the series of absolute values diverges.