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Prove these equations by using Induction and Pascal's equation or (1-1)^n and (1+1)^n

  1. Sep 4, 2011 #1
    1. The problem statement, all variables and given/known data
    Prove:
    The sum of r=0 to n [((-1)^r) * (nCr)] = 0.

    Prove:
    The sum of r=0 to n [nCr] = 2^n


    2. Relevant equations
    It says to consider (1-1)^n and (1+1)^n , but I have no idea what this is even relating to honestly.


    3. The attempt at a solution
    I need help getting started.
     
  2. jcsd
  3. Sep 4, 2011 #2

    HallsofIvy

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    Re: Prove these equations by using Induction and Pascal's equation or (1-1)^n and (1+

    You do know that
    [tex](a+ b)^n= \sum_{r=0}^n \left(\begin{array}{c}n \\ r\end{array}\right)a^{n-r}b^r[/tex]
    don't you?
     
  4. Sep 4, 2011 #3
    Re: Prove these equations by using Induction and Pascal's equation or (1-1)^n and (1+

    Yes I do, but I don't know how to apply it. I realize the (1-1)^n is the considered piece for the alternating series. But do I just Induction with it?
     
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