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Math Help - binomial Sum.

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    binomial Sum.

    Calculate Sum of \bf ^nC_{0}-^{n-1}C_{1}+^{n-2}C_{2}-^{n-3}C_{3}...........
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    Evaluating each term.

    \displaystyle =\frac{1}{0!}-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\dots
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    Quote Originally Posted by jacks View Post
    Calculate Sum of \bf ^nC_{0}-^{n-1}C_{1}+^{n-2}C_{2}-^{n-3}C_{3}...........
    \sum_{k=0}^n(-1)^k\binom{n}{k}=\sum_{k=0}^n\binom{n}{k}\cdot 1^{n-k}\cdot (-1)^k=\left(1+(-1)\right)^n = 0^n=0

    assuming 0\leq n\in\mathbb{N}
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