Erwin Harahap

do Now or Never

Berikan alsan serta bukti bahwa 0! = 1

Posted by Erwin on October 8, 2015

Jawab:

Berdasarkan definisi, kita ketahui bahwa:

1! = 1*1 = 1
2! = 2*1 = 2
3! = 3*2*1 = 6
4! = 4*3*2*1 = 24
… dst, hingga n dimana
n! = n*(n-1)*(n-2)* … * 3*2*1

atau bisa juga kita tulis:
n! = n*(n-1)!

Gunakan rumus diatas, untuk n = 1 berlaku:
1! = 1*(1-1)! = 1*0!
dari definisi awal, kita ketahui bahwa
1! = 1
atau
1*0! = 1
dengan demikian, maka 0! = 1

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