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Thread: Binomial expansion

  1. Jul 31st 2009, 03:30 PM #1
    gtaplayr
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    Binomial expansion

    Can anyone prove the binomial expansion:

    (x+y)^n = \sum \left(\begin{array}{c}n\\r\end{array}\right) x^r.y^{n-r}
    Last edited by gtaplayr; Jul 31st 2009 at 03:46 PM.
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  2. Jul 31st 2009, 03:52 PM #2
    Jhevon
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by gtaplayr View Post
    Can anyone prove the binomial expansion:

    (x+y)^n = \sum \left(\begin{array}{c}n\\r\end{array}\right) x^r.y^{n-r}
    this is certainly something that can be found all over the internet. see here
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  3. Jul 31st 2009, 11:01 PM #3
    CaptainBlack
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    Quote Originally Posted by gtaplayr View Post
    Can anyone prove the binomial expansion:

    (x+y)^n = \sum \left(\begin{array}{c}n\\r\end{array}\right) x^r.y^{n-r}
    You only need to prove:

    (1+x)^n=\sum_{r=0}^n {n \choose r} x^r

    and this can be done reasonably easily by induction.

    CB
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