\text { Investigate the behavior (convergence or divergence) of } \Sigma a_{n} \text { if } \text { (a) } \bar{a}_{n}=\sqrt{n+1}-\sqrt{n} \text { (b) } a_{n}=\frac{\sqrt{n+1}-\sqrt{n}}{n} \text { (c) }

a_{n}=(\sqrt[n]{n}-1)^{n} \text {; } \text { (d) } a_{n}=\frac{1}{1+z^{n}}, \text { for complex values of } z \text {, }