Question

Prove that 0!=1

FAST ASAP

Answer 1

It is pretty easy actually. I'm not going by the definition here. But this is still a mathematically correct solution.

1!= 1

2!= 1x2

3!= 1x2x3 and so on..

But notice how 3!= 2!x3

So (n+1)!= n!x(n+1) correct?

Now substitute n as 0, we get

1!=0!x1

Therefore, 0!=1!=1

If you wanna know more about this, try googling gamma function for factorials. There's an integral function which can be integrated for n=0 for x=0 to ∞

Answer 2

We know that :

n! = 1 × 2 × 3 × ......................  × n - 1  × n

( n - 1 ) × = 1  × 2 × 3 ................  × n - 2 × n - 1  

Divide these two equations :

n ! / ( n - 1 )! = ( 1 × 2 ........... n ) / ( 1 × 2 ........  n - 1 )

Cancel the terms :

==> n! / ( n - 1 )! = n

Putting n = 1 we get :

==> 1! / ( 1 - 1 )! = 1

==> 1 ! / 0 ! = 1

==> 0 ! = 1 ! / 1

==> 0 ! = 1 / 1

==> 0 ! = 1 [ P.R.O.V.E.D ]

Hope it helps :)

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