Answer
a) Diverges
b)Diverges
Work Step by Step
a) Factoring out the constant $ (\frac{2}{3}+\frac{1}{k})$ leaves
$$\Sigma^m_{k=1} [(\frac{2}{3}+\frac{1}{k})]$$
This is a p-series with p<1. p is not greater than 1, so the series diverges
b) Factoring out the constant $ (\frac{1}{3k+2}+\frac{1}{k^{3/2}})$ leaves
$$\Sigma^m_{k=1} [(\frac{1}{3k+2}+\frac{1}{k^{3/2}})]$$
This is a p-series with p<1. p is not greater than 1, so the series diverges
