Permutation proof

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October 26th 2010, 05:44 PM
guyonfire89

Permutation proof

I have a problem where the question is, Prove

$\frac{1}{2}P(2,1)+\frac{2}{3}P(3,2)+\frac{3}{4}(4, 3)+...+\frac{n}{n+1}P(n+1,n)=(n+1)!-1$

How do I start this? Do I use mathematical induction?
October 27th 2010, 07:02 AM
emakarov

Is $\displaystyle P(n,k)=\frac{n!}{(n-k)!}$ ? Then yes, the statement can be easily proved by induction.

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