1. Limited time only! Sign up for a free 30min personal 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!

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

    User Avatar
    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook