Mathematics

Problem

The series

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

is approximated by its fifth partial sum, which is

S_5\approx1.463611

. What is the greatest possible distance between

S_5

and the true value of the series? a)

0.040816

0.080000

0.055556

0.027778