formulario Taylor

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