Let Determine the least integer such that .

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let

S=\displaystyle\sum_{n=2}^{\infty} (-1)^{n}\dfrac{\ln n}{n^{2}}.

Determine the least integer

N

such that

|S-S_N|<5\times10^{-4}