e

Isaac Newton の binomial series

(x+y)^n = {n \choose 0}x^n y^0 + {n \choose 1}x^{n-1}y^1 + {n \choose 2}x^{n-2}y^2 + \cdots + {n \choose n-1}x^1 y^{n-1} + {n \choose n}x^0 y^n

x ＝1  , y ＝ 1n

   e＝ \lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}

 

{\displaystyle e=\exp 1=\sum _{n=0}^{\infty }{\frac {1}{n!}}}

 

     T.theodor