Find the smallest positive integer such that using the first terms of approximates…

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Find the smallest positive integer

N

such that using the first

N

terms of

\displaystyle\sum_{k=1}^{\infty}\frac{1}{k^{2}}

approximates the total sum to within

0.01