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谁能告诉我,数学中 e的由来?

来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/16 05:32:59
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 .
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