Mathematics

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.