common Maclaurin series

$$\begin{array}{rlrl}\frac{1}{1-x}& =\sum _{n=0}^{\infty }{x}^n& & =1+x+x^2+x^3+\dots \\ e^x& =\sum _{n=0}^{\infty }\frac{x^n}{n!}& & =1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots \\ \cos x& =\sum _{n=0}^{\infty }\frac{(-1{)}^n{x}^{2n}}{(2n)!}& & =1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\dots \\ \sin x& =\sum _{n=1}^{\infty }\frac{(-1{)}^{n-1}{x}^{2n-1}}{(2n-1)!}& & =x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\dots \\ \ln (1+x)& =\sum _{n=1}^{\infty }\frac{(-1{)}^{n-1}{x}^n}{n}& & =x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\dots \\ \arctan x& =\sum _{n=1}^{\infty }\frac{(-1{)}^{n-1}{x}^{2n-1}}{2n-1}& & =x-\frac{x^3}{3}+\frac{x^5}{5}-\frac{x^7}{7}+\dots \end{array}$$