1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why (1+1/n)^n goes to e as n goes to infinite?

  1. Dec 14, 2011 #1
    I uploaded a picture of my question. I am just wondering how to justify how (1 + 1/n)^n goes to e as n goes to ∞? How do you show this?
    Thanks!
     

    Attached Files:

  2. jcsd
  3. Dec 14, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You can if you take the log and then use l'Hopital's rule. On the other hand it might just be a definition of 'e'.
     
  4. Dec 14, 2011 #3
    You could alose plug in some very large values of n and see that it indeed approaches e (I was bored and did this myself a few days ago). This is the definition of e.
     
  5. Dec 15, 2011 #4

    Deveno

    User Avatar
    Science Advisor

    nevermind.
     
  6. Dec 15, 2011 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    How, exactly are you defining "e"? In many texts, e is defined by that limit.
     
  7. Dec 15, 2011 #6

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    It's more instructive to show that the sequence converges. Its limit is denoted by 'e' and is one of the most important real numbers in mathematics. Another interesting proof would be to show that the number, namely the limit, is irrational. Then transcendental.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook