Chapter 9, Problem 33RE

In parts (a)-(d), find the sum of the series by associating it with some Maclaurin series.

$\begin{array}{l}\text{(a)}\text{2+}\frac{4}{2!}+\frac{8}{3!}+\frac{16}{4!}+\mathrm{...}\\ \text{(b)}\pi -\frac{{\pi }^3}{3!}+\frac{{\pi }^5}{5!}-\frac{{\pi }^7}{7!}+\mathrm{...}\\ \text{(c)}\text{1}-\frac{e^2}{2!}+\frac{e^4}{4!}+\frac{e^6}{6!}+\mathrm{...}\\ \text{(d)}\text{1}-\ln \text{3+}\frac{{(\ln 3)}^2}{2!}-\frac{{(\ln 3)}^3}{3!}+\mathrm{...}\end{array}$