Prove, for any integer n:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum_{0\,\leq\,m\,< n/2}\,(-1)^m(n - 2m)^n\,^nC_m\ =\ 2^{n-1}\,n![/tex]

for example, 7^{7}- 5^{7}7 + 3^{7}21 - 1^{7}35

= 823543 - 546875 + 45927 - 35 = 304560 = 64 times 5040

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# Prove ∑ … = (2^n-1)n!

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