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Math Help - Permutation proof

  1. #1
    Junior Member
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    Sep 2010
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    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?
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  2. #2
    MHF Contributor
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    Is \displaystyle P(n,k)=\frac{n!}{(n-k)!}? Then yes, the statement can be easily proved by induction.
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