# Math Help - 2 questions on factorial

1. ## 2 questions on factorial

(1) Why is (r+1)r!=(r+1)!

(2)This is commonly asked : why is 0! =1 ??

2. Originally Posted by mathaddict
(1) Why is (r+1)r!=(r+1)!

(2)This is commonly asked : why is 0! =1 ??
$(r+1)r! = (r+1) \times r(r-1)(r-2)(r-3)\times ...\times 1$

$(r+1)! = (r+1)(r+1-1)(r+1-2)(r+1-3)\times ...\times 1 = (r+1)(r)(r-1)(r-2)\times ...\times 1$

See how they are identical?

Also. We know that $n!= n(n-1)(n-2)(n-3)...1$. This can be written $n! = n(n-1)!$

So, let's look at n = 1, knowing that $1! = 1$

$1! = 1(1-1)!$

$1 = 1(0)!$

$1 = 0!$.