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If n and k are positive integers, show...

If `n` and `k` are positive integers, show that `2^k(nC 0)(n k)-2^(k-1)(nC1)(n-1Ck-1)+2^(k-2)(nC2)((n-2k-2))_dot-...+(-1)^k(nCk)+(n-kC0)=(nC k)w h e r e(n C k)` stands for `^n C_kdot`

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