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"^(n)P(n)=1...

`"^(n)P_(n)=1`

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Prove that 1+1* ""^(1)P_(1)+2* ""^(2)P_(2)+3* ""^(3)P_(3) + … +n* ""^(n)P_(n)=""^(n+1)P_(n+1).

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

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If ""^(2n+1)P_(n-1) : ""^(2n-1)P_(n) =3 :5 the possible value of n will be :

The largest value of n in N for which (74)/(""^(n)P_(n)) gt (""^(n + 3)P_(3))/(""^(n +1)P_(n + 1)) is _______