زنجیرەی تایلۆر

${\displaystyle f(x)=f(x_{0})+{\frac {f'(x_{0})(x-x_{0})}{1!}}+{\frac {f''(x_{0})(x-x_{0})^{2}}{2!}}+{\frac {f'''(x_{0})(x-x_{0})^{3}}{3!}}+...}$ 

${\displaystyle f(x)=\sum _{n=0}^{\infty }{\frac {f^{(n)}(x_{0})}{n!}}(x-x_{0})^{n}}$ 

${\displaystyle f(x)=e^{2x}}$ 

${\displaystyle e^{2x}={\frac {(1)}{(e^{2})}}+{\frac {(2)(x+1)}{(1!)(e^{2})}}+{\frac {(2^{2})(x+1)^{2}}{(2!)(e^{2})}}+{\frac {(2^{3})(x+1)^{3}}{(3!)(e^{3})}}+...}$ 

${\displaystyle e^{2x}=\sum _{n=0}^{\infty }{\frac {(2)^{(n)}}{((n)!e^{2})}}(x+1)^{n}}$