I have a problem where the question is, Prove

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

How do I start this? Do I use mathematical induction?

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- Oct 26th 2010, 05:44 PMguyonfire89Permutation proof
I have a problem where the question is, Prove

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

How do I start this? Do I use mathematical induction? - Oct 27th 2010, 07:02 AMemakarov
Is $\displaystyle \displaystyle P(n,k)=\frac{n!}{(n-k)!}$? Then yes, the statement can be easily proved by induction.