Re: Mathematical induction!

Do you mean that (n+1)(n+2)...(2n) is divisible by 4? This is obvious because 2n is even and, since the number of factors is ≥ 3 for n ≥ 3, there is another even factor.

Re: Mathematical induction!

What, exactly, do you mean by ((n+1)(n+ 2)...(2n)) if n= 1? I see that, for example, if n= 3, then this is 4(5)(6) but what about n= 1? Is this "2" or "2(2)"? If the first, which is what I would think because 1+ 1= 2(1), the statement is not true:

But for n= 2, this is 3(4)(4) which is divisible by because it has a factor of 4. If , there are four consecutive numbers in that so at least one is divisible by 4.

Re: Mathematical induction!

Okay so here is a hopefully a bit better presentation of the assignment:

"Prove with mathematical induction that

is an integer when

First time using latex...

thank you for your help!

Re: Mathematical induction!

... and theres minor error in my first post. sorry bout that

Re: Mathematical induction!

I chose to write the induction hypothesis after looking at the first several statements:

We easily see that is true, so next I defined:

Now, adding to both sides of there results:

We have derived from thereby completing the proof by induction.