Ok_Scientist_691 | 1 points | Dec 03 2021 15:28:43

Can any Chinese math genius answer my question regarding the binomial expansion of e

https://i.redd.it/vpsmfo5zic381.png

[-] DecadeBodyBuilding | 12 points | Dec 03 2021 16:07:47

定义是e=lim（1+1/n）^n 你二项式展开不就是这个吗？ 你在证个鸡巴。

[-] [deleted] | 1 points | Dec 03 2021 16:16:46

[removed]

[-] Ok_Scientist_691 | 0 points | Dec 04 2021 05:35:25

我是問當k 很大的時候，為何1/k!之前的項可以當作1

[-] DecadeBodyBuilding | 1 points | Dec 04 2021 05:41:06

也没人当成1啊, 有哪本书证明e等于那个求和是直接写前面的项当成1所以能相等吗。

[-] bakemonor | 7 points | Dec 03 2021 15:47:54

good cock difficult

[-] Ok_Scientist_691 | 2 points | Dec 03 2021 15:49:59

好雞巴難？

I use zhinabaidu translate.

[-] Top_Yellow_4690 | 7 points | Dec 03 2021 15:51:10

充其量就是e^x 泰勒展开取x=1。

[-] Ok_Scientist_691 | 1 points | Dec 03 2021 15:52:48

你沒答鄙人問題啊

[-] Top_Yellow_4690 | 1 points | Dec 03 2021 15:57:21

我一般是把极限写进去，先求极限，再求和。

[-] Top_Yellow_4690 | 1 points | Dec 03 2021 16:00:05

我学工科的，不懂严格证明，但做题时可以这么写。

[-] 1q956_ | 4 points | Dec 03 2021 16:02:24

原式=∑n！/ n\^k（n-k）！k！

=∑ Cnk/n\^k

=∑ Cnk* n\^(n-k) /n\^n

=∑ Cnk* n\^(n-k)*1\^k /n\^n

=(1+n)\^n/n\^n=(1+1/n)\^n

n-&rt;∞ 原式-&rt;e

[-] 1q956_ | 2 points | Dec 03 2021 16:03:15

这个说法可以解决op的问题么

[-] XWN_BS | 4 points | Dec 03 2021 17:50:54

数学tv

[-] Ok_Scientist_691 | 1 points | Dec 03 2021 15:30:14

My thought is:

&rt; Since k will range from 0 to n, so when k is sufficiently large, say 𝑛/2,
then( 𝑛−𝑘+1)/𝑛 won't simply be 1.

What is my mistake? Should this question violate the rules of this sub. I will remove it. :((((

[-] 1q956_ | 3 points | Dec 03 2021 15:51:31

如果你把k取到n/2的话 那右边的1/k！就趋向于0了

[-] Specific_Job6294 | 2 points | Dec 03 2021 17:54:47

k不能取n/2，无穷不允许这样。

[-] [deleted] | 1 points | Dec 03 2021 16:12:53

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[-] Press_F_Pay_Respect | 1 points | Dec 03 2021 17:14:23

这种式子里的k取你妈值呢？就一个dummy variable表示从0乘到n而已。

要证这种式子需要数学归纳法

[-] [deleted] | 1 points | Dec 03 2021 17:48:36

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[-] Googrosoft | 1 points | Dec 03 2021 18:32:45

Switch the sum and lim sign. All the terms ahead of 1/k! converge at 1 when n-&rt;inf since they always have the same highest order of n. And obviously sum(1/k!)=e when k runs from 0 to n (inf).

[-] plsmxy | 1 points | Dec 03 2021 15:39:04

/homeworkhelp

[-] Ok_Scientist_691 | 1 points | Dec 03 2021 15:47:26

不是功課 支那老師根本不會管我這些無聊無意義的問題

[-] [deleted] | 1 points | Dec 03 2021 15:55:46

[deleted]

[-] XiXiP | 1 points | Dec 03 2021 16:02:58

lim_{n-&rt;\infty} (n+k-1)/n = lim_{n-&rt;\infty} (n)/n

[-] FrostingCreative1328 | 1 points | Dec 03 2021 16:24:24

check: https://math.stackexchange.com/questions/860796/how-to-show-that-sum-n-0-infty-frac-1n-e

You should be able to find it in an elementary real analysis textbook. e.g. Rudin

[-] Ok_Scientist_691 | 1 points | Dec 03 2021 17:26:37

thanks for your help.

[-] poiulkjh87 | 1 points | Dec 03 2021 17:23:07

這什麼鬼

[-] Ok_Scientist_691 | 1 points | Dec 03 2021 17:27:05

支鬼

[-] poiulkjh87 | 1 points | Dec 03 2021 17:29:37

Where did you see this problem ? college calculus class or analysis class?

[-] Ok_Scientist_691 | 1 points | Dec 03 2021 18:06:41

出錯了嗎

[-] poiulkjh87 | 1 points | Dec 03 2021 18:13:54

Nothing just curious

[-] No-Hunt-4486 | 1 points | Dec 03 2021 17:35:47

明天细看，今晚娱乐一下

[-] PillowDoctor | 1 points | Dec 03 2021 17:54:29

不会做微积分bc，屠了屠了

[-] New-Edge-8765 | 1 points | Dec 03 2021 19:02:49

什么做题家tv

[-] CommieEater | 1 points | Dec 04 2021 05:21:19

Me and my gang are literally illiterate so I'd suggest you go and consult with Dr Xi directly

[-] cprwwww | 1 points | Dec 04 2021 05:44:06

英语不好请见谅。

因为k与n不是一起趋于无穷的，是将k先固定为一个实数，使n趋于无穷，再将k趋于无穷