Show that `n{P{P(P(varphi))}}=4.`

Show that n[P[P.(P(phi)))=4

Show that n(P(P(P( phi))))=4

Show that (n+1)(""^(n)P_(r)) = (n-r+1)[""^(n+1)P_(r)]

Let P (n) denote the statement : “ 2^n gen ! ". Show that P(1), P(2) and P(3) are true but P(4) is not true.

Let P(n) denote the statement: 2^(n)ge n! .Show that P(1),P(2),P(3) are true butP(4) is not true.

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

Show that P(m,1)+P (n,1)=P(M+n,1) for all positive integers m, n.

Show that (n +1) ("^(n)P_r) = (n - r + 1) ["^((n +1))P_r]

If the coefficients of the pth , (p+1)and (p+2) terms in the expansions of (1+x)^(n) are in A.P , show that , n^(2)-n(4p+1)+4p^(2)-2=0

Show that ""^(n)P_(n)=2""^(n)P_(n-2)