I have to prove the following theorem:
Prove that the product of $r$ consecutive positive integers in divisible by $r!$
I am having a hard time getting a generalization down for the full set of real numbers, if I start from 1 and work up to r, I have the following:
Can easily prove the base case of this, (n=1), and then go in to prove:
Expand that out and get:
Can say that the product of the first $r$ elements in equal to $r!k$ by our base case. Leaving using with:
Not sure where I can go from here, n is the integer that we start at, so how can I get it to work out to be equal to our induction hypothesis?