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Homework Help: 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

    morphism

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    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.
     
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