Grade 12Algebra

Why zero factorial is 1 ?

please explain with proof ....

Thanks...

Hasan Ali

14 Years agoGrade 12

2 Answers

Aman Bansal

Approved Tutor Answer14 Years ago

Dear HAsan,

If n! is defined as the product of all positive integers from 1 to n, then:
1! = 1*1 = 1
2! = 1*2 = 2
3! = 1*2*3 = 6
4! = 1*2*3*4 = 24
...
n! = 1*2*3*...*(n-2)*(n-1)*n
and so on.
Logically, n! can also be expressed n*(n-1)! .

Therefore, at n=1, using n! = n*(n-1)!
1! = 1*0!
which simplifies to 1 = 0!

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Aman Bansal

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