Let `nP_r` denote the number of permutations of n differenttaken r at a time. Then, prove that `1+1*1P_1+2*2P_2+3*3P_3+......+n*nP_n=n+1P_(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.^(1)P_(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

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

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

If the number of permutations of n different things taken r at a time be denoted by nP_(r) show that (nP_(1))/(1!)+(nP_(2))/(2!)+(nP_(3))/(3!)+......+(nP_(n))/(n!)=2^(n)-1

If the number of permutations of n different things taken r at time be denoted by .^(n)P_(r) , show that , (.^(n)P_(1))/(1!)+(.^(n)P_(2))/(2!)+(.^(n)P_(3))/(3!)+...+(.^(n)P_(n))/(n!)=2^(n)-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)!