中四附加數

2007-09-13 5:57 am
Prove that 100!=2^50(1*3*5*7.......*99 )*50!

回答 (1)

2007-09-13 6:01 am
✔ 最佳答案
100! = 1x2x3x...x100
=(1x3x5x...x97x99)x(2x4x6x...x98x100)
=(1x3x5x...x97x99)x[(2x1)x(2x2)x(2x3)x...x(2x49)x(2x50)]
=(1x3x5x...x97x99)x2^50x(1x2x3x...x49x50)
=2^50(1x3x5x...x97x99)50!
參考: me


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