Successive partial sums of the series are used for approximation

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

Problem

Successive partial sums

S_N

of the series

\displaystyle \sum_{n=1}^{\infty} \tfrac{1}{n^{2}}

are used for approximation. Find the smallest integer

N

for which

|S_{N+1} - S_N| < 0.0001