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2^n Induction

  1. Aug 9, 2007 #1
    How can I show that

    [tex]1+\frac{n}{1!}+\frac{n(n-1)}{2!}+\frac{n(n-1)(n-2)}{3!}+...= 2^{n} [/tex]

    This comes from proving that the power set of a set with n elements is [tex]2^{n}[/tex].

    I got so far that nCn+nC(n-1)+ ... = what I have above. Now for the induction...
  2. jcsd
  3. Aug 9, 2007 #2


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    Hint: What's the binomial expansion of (1 + 1)^n?
  4. Aug 9, 2007 #3
    of course, thanks
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