...求证:1. (k+1)!=(k+1)k! 2. (2n)!/2n!=n(2n-1)(2n-2)...(n+1...
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发布时间：2024-10-24 14:30
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热心网友
时间：2024-10-26 18:43
（k+1)!=(k+1)[k(k-1)(k-2).....2x1
=(k+1)k!
(2n)!=2n(2n-1)(2n-2)(2n-3).....[2n-(n-1) ]（2n-n）(n-1)(n-2)....2x1
=2n(2n-1)(2n-2)(2n-3)......[2n-(n-1) ]n!
=2n(2n-1)(2n-2)(2n-3)......（n+1）n!
∴ (2n)!/2n!=n(2n-1)(2n-2)...(n+1)
