Mathematics

Problem

Let

S=\displaystyle\sum_{n=1}^{\infty}\frac{1}{n^{2}}

and let

S_{N}=\sum_{n=1}^{N}\frac{1}{n^{2}}

. Which expression gives an upper bound for the remainder

R_{N}=S-S_{N}

? a)

\dfrac{1}{N^{2}}

\dfrac{1}{N}

\dfrac{1}{N+1}

\dfrac{1}{(N+1)^{2}}