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點解 0! = 1 ?
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最佳解答:
By the definition of nCr nCr=n!/[(n-r)!xr!] the first term of the binomial expression (x+1)^n is (nCn)x^n =n!/n!(0!)x^n If 0! <> 1 , then the first and the last term 's coeff. is not 1 , and it is not true. So 0! must equal to 1 , you may treat it as definition too.
其他解答:
除左上面所答的, recurrence relation 圖片參考：http://upload.wikimedia.org/math/0/4/f/04f0de9cd29fc21e0bb3bf57a31a760b.png works for n = 0 之外. 我試下用中五學生可以理解的例子來答! nCr, 學左啦! nCr = n! / (r!)(n-r)! 咁如果n=0, r又=0, 圖片參考：http://upload.wikimedia.org/math/6/1/c/61c7fc770aebe276db140466fabdd954.png 雖然用nCr來解factorial,唔可以叫好好. 不過, 希望你可以明啦!|||||呢個係定義，無得解 ... 有左呢個定義，可以帶來一些運算上的便利，如 (n + 1)! = n! * (n + 1) ，或者其他 combination / permutation 的計算。
點解 0! = 1 ?
發問:
此文章來自奇摩知識+如有不便請留言告知
點解 0! = 1 ? 我f.5,, 請簡單dd解釋~ 謝最佳解答:
By the definition of nCr nCr=n!/[(n-r)!xr!] the first term of the binomial expression (x+1)^n is (nCn)x^n =n!/n!(0!)x^n If 0! <> 1 , then the first and the last term 's coeff. is not 1 , and it is not true. So 0! must equal to 1 , you may treat it as definition too.
其他解答:
除左上面所答的, recurrence relation 圖片參考：http://upload.wikimedia.org/math/0/4/f/04f0de9cd29fc21e0bb3bf57a31a760b.png works for n = 0 之外. 我試下用中五學生可以理解的例子來答! nCr, 學左啦! nCr = n! / (r!)(n-r)! 咁如果n=0, r又=0, 圖片參考：http://upload.wikimedia.org/math/6/1/c/61c7fc770aebe276db140466fabdd954.png 雖然用nCr來解factorial,唔可以叫好好. 不過, 希望你可以明啦!|||||呢個係定義，無得解 ... 有左呢個定義，可以帶來一些運算上的便利，如 (n + 1)! = n! * (n + 1) ，或者其他 combination / permutation 的計算。
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