Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

tunahan

  • 2 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
  1. tunahan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I thought it should be \[\lim{n \to \infty}(1-0)^{n}\]

  2. meera_yadav
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 4

    hiii, 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 + (1-x)/2! + (1-x)(1-2x)/3!+............ now apply limit x tending to 0 you'll get : 1+1+1/2!+ 1/3!+.......... = e similarly for \[(1-x)^{x}\] we get e-1 :)

  3. tunahan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can we find this rule in internet, is it possible to send a link for it ?

  4. meera_yadav
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 4

    yeah you can google that out !! I answerd that on what I recently studied :)

  5. tunahan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok i think your answer is good enough, but to understand better i need to read once more i think from other source..

  6. tunahan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what is this number name \[e^{-1}\] ?

  7. meera_yadav
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 4

    it's actually exponential to the power -1... we write it as " e " it's value approximately equals to 2.7

  8. tunahan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok..

  9. meera_yadav
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 4

    e-1 = 1/e is it more clear now..?

  10. tunahan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok thank you very much, its clearer

  11. meera_yadav
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 4

    we can expand e^x as 1+ x/1! + x^2/2! + x^3/3!+......

  12. tunahan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm...

  13. tunahan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok thank you meera now its much clearer, thanks for your efforts

  14. meera_yadav
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 4

    :)

  15. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.