Let and let . Which expression gives an upper bound for the remainder…

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

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}}

(b)

\dfrac{1}{N}

(c)

\dfrac{1}{N+1}

(d)

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