谁能告诉我,数学中 e的由来?

e的来源有二：
来源一：
楼主先算一算以下各式,就能明白e为何物：
(1 + 1/1)^1 = 1
(1 + 1/2)^2 =
(1 + 1/3)^3 = 2。37037037。
(1 + 1/4)^4 =
(1 + 1/5)^5 = 2。48832000
(1 + 1/10)^10 =
(1 + 1/20)^20 = 2。653297705。
(1 + 1/50)^50 =
(1 + 1/100)^100 = 2。704813829。
(1 + 1/200)^200 =
(1 + 1/500)^500 = 2。715568521。
(1 + 1/1000)^1000 =
(1 + 1/5000)^5000 = 2。71801005。
(1 + 1/10,000)^10,000 =
(1 + 1/50,000)^50,000 = 2。718254646。
(1 + 1/100,000)^100,000 =
(1 + 1/500,000)^500,000 = 2。71827911。
(1 + 1/1,000,000)^1,000,000 =
(1 + 1/5,000,000)^5,000,000 = 2。718281557。
(1 + 1/10,000,000)^10,000,000 =
(1 + 1/50,000,000)^50,000,000 = 2。718281801。
(1 + 1/100,000,000)^100,000,000 =
(1 + 1/500,000,000)^500,000,000 = 2。718281826。
(1 + 1/1,000,000,000)^1,000,000,000 =
(1 + 1/10,000,000,000)^10,000,000,000 = 2。718281828。
。
这样下去的值,就是 e。
来源二：
1=1
1+1/1!
1+1/1!+1/2!=2。5
1+1/1!+1/2!+1/3!
1+1/1!+1/2!+1/3!+1/4!=2。7083333333。
1+1/1!+1/2!+1/3!+1/4!+1/5!
1+1/1!+1/2!+1/3!+1/4!+1/5!+1/6!=2。718055556。
1+1/1!+1/2!+1/3!+1/4!+1/5!+1/6!+1/7!
1+1/1!+1/2!+1/3!+1/4!+1/5!+1/6!+1/7!+1/8!=2。71827877。
1+1/1!+1/2!+1/3!+1/4!+1/5!+1/6!+1/7!+1/8!+1/9!
1+1/1!+1/2!+1/3!+1/4!+1/5!+1/6!+1/7!+1/8!+1/9!+1/10!=2。718281801。。。
这样下去,一样得到 e 。