Let . Which statement about is…

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

Problem

Let

S=\displaystyle\sum_{n=2}^{\infty} \dfrac{\ln n}{n^{2}}

. Which statement about

S

is true? (a)

S

diverges since the terms behave like

1/n

for large

n

.},{ (b)

S

converges conditionally but not absolutely. (c)

S

converges because

\displaystyle\int_{2}^{\infty}\dfrac{\ln x}{x^{2}}\,dx

is finite. (d)

S

diverges because

\displaystyle\int_{2}^{\infty}\dfrac{\ln x}{x^{2}}\,dx

is infinite.