Mathematics

Problem

The series

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

converges. What is the least integer

n

for which the absolute error

|S-S_n|

is guaranteed to be less than

0.0005

? a) 45 b) 44 c) 38 d) 43