Consider the series:

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^p},$ for $p>0$

$(a)$ Use the left$-$endpoint approximation $of{\displaystyle \underset{1}{\overset{N}{}}}\frac{1}{x^p}dxto$ obtain a lower bound for the

partial sum $S_N.$

$(b)$ Use the right$-$endpoint approximation $of{\displaystyle \underset{1}{\overset{N}{}}}\frac{1}{x^p}dxto$ obtain $an$ upper bound for the

partial sum $S_N.$