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!

Maths project

  1. Nov 6, 2008 #1
    Maths project proving lim n-infinity (1+x/n)^n = exp(x)

    1. The problem statement, all variables and given/known data
    project aiming to show that limn→∞(1+x/n)^n = exp(x)

    2. Relevant equations

    3. The attempt at a solution
    I have no Idea, is there any chance someone could give me some sort of clue?
    Last edited: Nov 6, 2008
  2. jcsd
  3. Nov 6, 2008 #2
    here is my attempt so far,
    (a+b)^n= (n) a^n + (n) a^n-1 b + (n) a^n-2 b^2 + ........... (n) b^n
    (0) (1) (2) (n)
  4. Nov 6, 2008 #3
    oh please help me!!!
    I don't know what to do!!!
    should I use (a+b)(a+b)^n-1?
  5. Nov 6, 2008 #4
    Try rewriting your limit as [tex]\lim_{n\rightarrow\infty}\exp\left[\ln\left(\left(1+\frac{x}{n}\right)^{n}\right)\right][/tex].

    From there, I believe, you should try to get it into a form where L'Hôpital's rule will apply.

    edit :: Yup, I just worked it out and this works.
    Last edited: Nov 6, 2008
  6. Nov 7, 2008 #5


    User Avatar
    Science Advisor
    Homework Helper

    How is exp(x) defined for you?

    If it's defined as the inverse of the natural log, then bowma166's method is a good way to approach this problem. But be careful: first you must show that the limit

    [tex]\lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n[/tex]

    exists, for all x.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Maths project
  1. Optimization Project (Replies: 0)

  2. Defining Projection (Replies: 0)

  3. Orthogonal projection (Replies: 13)

  4. Projection Matrices (Replies: 1)