Let be the fifth partial sum of the series

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

Problem

Let

S_5

be the fifth partial sum of the series

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

. Determine numerical upper and lower bounds for the exact sum of the series using

S_5

. Express each bound to six decimal places.