\(\frac{1}{1-x}=1+x+x^2+x^3+...+x+o(x^n)\)
\(\frac{1}{1+x}=1-x+x^2-x^3+...+(-1)^nx^n+o(x^n)\)
\((1+x)^{\alpha}=1+\alpha x +\binom{\alpha}{2}x^2+ \binom{\alpha}{3}x^3+...+\binom{\alpha}{n}x^n+o(x^n)\)
\(ln(1-x)=-x-\frac{x^2}{2}-\frac{x^3}{3}-\frac{x^4}{4}+...+o(x^n)\)
\(arctan(x)=x-\frac{x^3}{3}+\frac{x^5}{5}+...+(-1)^{n}\frac{x^{2n+1}}{2n+1}+o (x^{2n+1})\)
\(e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...+\frac{x^n}{n!}+o(x^n)\)
\(ch(x)=1+\frac{x^2}{2!}+\frac{x^4}{4!}+...+\frac{x^2n}{2n!}+o(x^{2n})\)
\(sh(x)=x+\frac{x^3}{3!}+\frac{x^5}{5!}+...+\frac{x^{2n+1}}{(2n+1)!}+o(x^{2n+1})\)
\(cos(x)=1-\frac{x^2}{2!}+\frac{x^4}{4!}+...+(-1)^n\frac{x^{2n}}{(2n)!}+o(x^{2n})\)
\(sin(x)=x-\frac{x^3}{3!}+...+(-1)^n\frac{x^{2n+1}}{(2n+1)!}+o(x^{2n+1})\)
\(tan(x)=x+\frac{1}{3}x^3+\frac{2}{15}x^5+o(x^5)\)
