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Math Help - Help in binomial theorem

  1. #1
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    Help in binomial theorem

    How can i calculate this sum?

    Thanks for any kind of help.
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  2. #2
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    Remember, (1+x)^m = \sum_{j=0}^m x^j {m\choose j}.

    This sum can be written as, \sum_{k=0}^n \sum_{i=0}^k \frac{n!}{k!(n-k)!}\cdot \frac{k!}{i! (k-i)!} (-3)^i = \sum_{k=0}^n \sum_{i=0}^k {n\choose k}\boxed{ {k\choose i} (-3)^i }

    Using the formula above on boxed term we get, \sum_{k=0}^n{n\choose k} (-2)^k = (-1)^n
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