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Homework Help: Binomial expansion

  1. Jul 13, 2010 #1
    How is

    [tex]1+p+\frac{p^2}{2!}+\frac{p^3}{3!}+...=e^p[/tex] ?
     
  2. jcsd
  3. Jul 13, 2010 #2

    Mentallic

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    Homework Helper

    I know it has to do with taylor expansions, but I've never studied this so I can't answer your question. I'd also like to see a proof for this so this is like some pointless post I'm making so I can subscribe to this thread :biggrin:
     
  4. Jul 13, 2010 #3
    Depends how you define e^p. You could just define it as the power series. However, I'm assuming you are using something like...

    [tex]
    e^p = \lim_{n \rightarrow \infty} (1 + \frac{p}{n})^n
    [/tex]

    Try using the binomial theorem on the right side, then take the limit.
     
  5. Jul 13, 2010 #4

    LCKurtz

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    You just show the remainder upon approximating it with the first n terms goes to zero as n --> infinity. See, for example,

    http://en.wikipedia.org/wiki/Taylor's_theorem
     
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