Prove that `.^(n-1) P_r+r .^(n-1) P_(r-1) = .^nP_r`

Prove that .^(n-1)P_(r)+r.^(n-1)P_(r-1)=.^(n)P_(r)

Prove that .^nP_r = ^(n-1)P_r + r^(n-1)P_(r-1)

Prove that: ""^(n-1)P_r=(n-r)* ""^(n-1)P_(r-1)

Prove that : ^nP_r= "^(n-1)P_r+r ^(n-1)P_(r-1) , for all natural numbers n and r for which the symbols are defined.

Prove that .^(n)P_(r)=.^(n-1)P_(r)+r.^(n-1)P_(r-1) .

Prove that ^nP_r= ^(n-1)P_r+r^(n-1)P_(r-1) (notation used are in their usual meaning).

If show that "^(n-1)P_r = (n-r).^(n-1)P_(r-1)

What is ""^(n-1)P_(r )+ ""^(n-1)P_(r-1) ?

Prove that: (i) (.^(n)P_(r))/(.^(n)P_(r-2)) = (n-r+1) (n-r+2)

Show that , .^(n)P_(r)=n.^(n-1)P_(r-1)=(n-r+1).^(n)P_(r-1) .