This is for high school but I suppose it is not studied in most high schools so I'll post it here. I don't know where to begin.

Prove that

Any help will be appreciated

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- Nov 4th 2008, 09:33 PMfobos3Factorial gamma function
This is for high school but I suppose it is not studied in most high schools so I'll post it here. I don't know where to begin.

Prove that

Any help will be appreciated - Nov 4th 2008, 10:38 PMChris L T521
From looking at it, I think the best way would be to prove this by mathematical induction:

First, show that this is true for N=1:

But , Thus

Now,

------------------------------------

Since we've shown this holds for N=1, Now we assume it holds for N=K

The hard [and really messy part] is to show it holds for N=k+1.

This means that

Note that

So

Knowing that , we see that

We can further simplify

Since

Thus, we need to show that

Let's get the left side to look like the right side:

This completes the inductive step.

(Whew)

Does this make sense? Hopefully you can follow what I did... (Nod)

--Chris

P.S. I wonder if anyone knows of a shorter way!?!?!?! (Wondering) - Nov 4th 2008, 11:06 PMfobos3
- Nov 5th 2008, 01:10 AMNonCommAlg
using the basic identity: we will have:

now the sum in the right hand side of (1) is a nice telescoping sum. thus (1) gives us:

finally multiplying both sides of (2) by gives us: which completes the proof because the

nice looking right hand side of my identity is equal to the weird looking right hand side of your identity! (Nod)