Chapter 11.2, Problem 1E

To determine

The formula of the general term $a_n$ of the following infinite series

(a) $\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\mathrm{...}$

(b) $\frac{1}{1}+\frac{5}{2}+\frac{25}{4}+\frac{125}{8}+\mathrm{...}$

(c) $\frac{1}{1}-\frac{2^2}{2.1}+\frac{3^3}{\mathrm{3.2.1}}-\frac{4^4}{\mathrm{4.3.2.1}}+\mathrm{...}$

(d) $\frac{2}{1^2+1}+\frac{1}{2^2+1}+\frac{2}{3^2+1}+\frac{1}{4^2+1}+\mathrm{...}$