(2) Test each of the following series for convergence: \text { (a) } \sum_{k=1}^{\infty} \frac{\sqrt{k+1}-\sqrt{k}}{k} \text { (b) } \sum_{k=1}^{\infty}(\sqrt[b]{k}-1)^{k} \text { (c) } \sum_{k=1}^{\infty} \sin \left(\frac{\ln k}{k^{2}}\right) \text {

(d) } \sum_{k=1}^{\infty} \frac{1}{k} \ln \left(1+\frac{1}{k}\right)