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Binomial Theorem

  1. Jun 1, 2009 #1

    All we know the Binomial Theorm which may be stated mathematically as:

    [tex]\left(x+y\right)^n=\sum_{k=0}^n{n\choose k}y^k\,x^{n-k}[/tex]

    Now suppose that we have the following mathematical expression:

    [tex]\sum_{k=0}^{n}{n\choose k}\,(-1)^k[/tex]

    if we substitute x=1 and y=-1 in the first equation we get the second. Is that mean the second equation is essentially zero, since [tex](1-1)^n=0[/tex]??

  2. jcsd
  3. Jun 1, 2009 #2
    Yes, indeed, unless n = 0.
  4. Jun 1, 2009 #3
    Why? In the case that n = 0, what will be the answer? 1?
  5. Jun 1, 2009 #4
    00 is not well-defined and neither is 0Ck for any k <> 0 (although there are generalizations that extend the domain beyond the definition using just factorials).
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