Science:Math Exam Resources/Courses/MATH101/April 2015/Question 05 (b)/Statement

The series $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{(2n+1)^{2}}}$ converges to some number S (you don’t have to prove this). According to the Alternating Series Estimation Theorem, what is the smallest value of n for which the nth partial sum of the series is at most ${\frac {1}{100}}$ away from S? For this value of n, write out the nth partial sum of the series.