A community for students.
Here's the question you clicked on:
 0 viewing
tunahan
 3 years ago
Why \(lim_{n \to \infty}(1\frac{1}{n})^{n} = e^{1} \) ?
OR How can i find this rule, whats it name ?
tunahan
 3 years ago
Why \(lim_{n \to \infty}(1\frac{1}{n})^{n} = e^{1} \) ? OR How can i find this rule, whats it name ?

This Question is Closed

tunahan
 3 years ago
Best ResponseYou've already chosen the best response.0I thought it should be \[\lim{n \to \infty}(10)^{n}\]

meera_yadav
 3 years ago
Best ResponseYou've already chosen the best response.4hiii, binomial expansion of \[(1+x)^{n}\] substitute for n=1/x you'll get binomial expansion as : \[(1+x)^{1/x}\] = 1+ x*1/x + (1x)/2! + (1x)(12x)/3!+............ now apply limit x tending to 0 you'll get : 1+1+1/2!+ 1/3!+.......... = e similarly for \[(1x)^{x}\] we get e1 :)

tunahan
 3 years ago
Best ResponseYou've already chosen the best response.0can we find this rule in internet, is it possible to send a link for it ?

meera_yadav
 3 years ago
Best ResponseYou've already chosen the best response.4yeah you can google that out !! I answerd that on what I recently studied :)

tunahan
 3 years ago
Best ResponseYou've already chosen the best response.0ok i think your answer is good enough, but to understand better i need to read once more i think from other source..

tunahan
 3 years ago
Best ResponseYou've already chosen the best response.0what is this number name \[e^{1}\] ?

meera_yadav
 3 years ago
Best ResponseYou've already chosen the best response.4it's actually exponential to the power 1... we write it as " e " it's value approximately equals to 2.7

meera_yadav
 3 years ago
Best ResponseYou've already chosen the best response.4e1 = 1/e is it more clear now..?

tunahan
 3 years ago
Best ResponseYou've already chosen the best response.0ok thank you very much, its clearer

meera_yadav
 3 years ago
Best ResponseYou've already chosen the best response.4we can expand e^x as 1+ x/1! + x^2/2! + x^3/3!+......

tunahan
 3 years ago
Best ResponseYou've already chosen the best response.0ok thank you meera now its much clearer, thanks for your efforts
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.