Prove the following: `P(n , n)=2P(n , n-2)`

Prove the following: P(n , n)=P(n , n-1)

Prove the following: P(n,n)=P(n,n-1)

Prove the following: P(n , r)=P(n-1, r)+rdotP(n-1,\ r-1)

Prove the following: P(n,r)=P(n-1,r)+rdot P(n-1,r-1)

Prove that P(n,n)=2.P(n,n-2)

By using the principle of mathematical induction , prove the follwing : P(n) : 2 + 4+ 6+ …..+ 2n =n(n+1) , n in N

Prove that : P(n,n)= 2P (n,n -2)

Prove that P(n,n) = P(n,n-1)

Consider the following statement : P(n):A^n=[[1+2n,-4n],[n,1-2n]] for all ninN Write P(1) .

Prove that : (i) ""^(n)P_(n)=2""^(n)P_(n-2) (ii) ""^(10)P_(3)=""^(9)P_(3)+3""^(9)P_(2) .