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Let .^(n)P(r) denote the number of per...

Let `.^(n)P_(r)` denote the number of permutations of n different things taken r at a time . Then , prove that `1+1.^(1)P_(1)+2.^(2)P_(2)+3.^(3)P_(3)+...+n.^(n)P_(n)=.^(n+1)P_(n+1)`.

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