关于自然底数e的由来

Question

关于自然底数e的由来

Answer 1

(1+1/1)^1 = 2
(1+1/2)^2 = 2.25
(1+1/3)^3 = 2.37037037
(1+1/4)^4 = 2.44140625
(1+1/5)^5 = 2.48832
(1+1/10)^10 = 2.59374246
(1+1/20)^20 = 2.65329771
(1+1/50)^50 = 2.69158803
(1+1/100)^100 = 2.70481383
(1+1/500)^500 = 2.71556852
(1+1/1000)^1000 = 2.716923932
(1+1/10,000)^10,000 = 2.718145927
(1+1/100,000)^100,000 = 2.718268237
(1+1/1,000,000)^1,000,000 = 2.718280469
(1+1/10,000,000)^10,000,000 = 2.718281693
(1+1/100,000,000)^100,000,000 = 2.718281815
(1+1/1,000,000,000)^1,000,000,000 = 2.718281827
(1+1/10,000,000,000)^10,000,000,000 = 2.718281828
.
特点：
1、递增序列；
2、收敛,有上限；
3、无限不循环小数.
所以：定义为 e
重要性：
1、没有e,微积分公式将困难重重；
2、没有e,虚数的运算将寸步难行；
3、没有e,就没有指数增长率,也没有指数衰减率,就没有办法将自然界的
许许多多规律进行统一归纳处理.