Chapter 9.4, Problem 8ES

Confirm that the integral test is applicable and use it to determine whether the series converges.

$\left(\text{a}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{k}{1+k^2}}\left(\text{b}\right){\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{1}{{\left(4+2k\right)}^{3/2}}}$