How can I simplify this factorial expression?

Thread starter Flappy
Start date Dec 9, 2008
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Factorial

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The discussion revolves around simplifying the factorial expression (kn)!/(kn+k)!. The initial thought was that the expression simplifies to 1/(kn+k), but the correct simplification involves recognizing that (kn+k)! expands to include multiple terms. The book's answer indicates that the correct simplification is 1/((kn+k)(kn+k-1)...(kn+1)), which accounts for all k numbers between kn and kn+k. Understanding the factorial expansion is crucial for arriving at the correct result. The key takeaway is that there are k terms in the denominator that must be included in the simplification process.

Dec 9, 2008

Flappy

Homework Statement

\frac{(kn)!}{(kn+k)!}

I was thinking:

(kn)! = 1*2*3...(kn)
(kn+k)! = 1*2*3...(kn)(kn+k)

and I would be left with 1/kn+k

But my book has the answer as:
\frac{1}{(kn+k)(kn+k-1)...(kn+1)}

How can I arrive to that?

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Dec 9, 2008

mutton

There are k numbers between kn and kn + k, not just one.

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