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

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

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

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)

prove that 1P_(1)+2.2P_(2)+3.3P_(3)+.......+n.nP_(n)=(n+1)P_(n+1)-1

If P_(m) stands for mP_(m), then prove that: 1+1.P_(1)+2.P_(2)+3.P_(3)+...+n.P_(n)=(n+1)!

Show that 1+^1P_1+2.^2P_2+3.^3P_3+....+n.^nP_n=^(n+1)P_(n+1) .

Prove that: 1.P (1,1)+2.P(2,2)+3.P(3,3)+...+n.P(n,n)=P(n+1,n+1)-1

if ^(n)P_(5):^(n)P_(3)=2:1, then n

Prove that ""^(2n+1)P_(n-1)=((2n+1)!)/((n+2)!) and ""^(2n-1)P_n=((2n-1)!)/((n-1)!)

The value of ""^(n)P_(1)+(""^(n)P_(2))/(2!)+(""^(n)P_(3))/(3!)+......+(""^(n)P_(n))/(n!)