`2.^(n)P_(3)=^(n+1)P_(3)`

If .^(n-1)P_(3):^(n+1)P_(3)=5:12, find n

Find the value of n from each of the following: (i) 10 .^(n)P_(6) = .^(n+1)P_(3) (ii) 16.^(n)P_(3) = 13 .^(n+1)P_(3)

If .^(n+1)P_(3)=10.^(n-1)P_(2) , find n.

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) .

Find n if .^(n-)P_(3): .^(n)P_(4) = 1:9 .

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

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

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