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

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

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

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

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

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

Given that P(n, r)=n(n-1)(n-2) ….to r factors If P(n, 4) = 20 P(n, 2), find n

If P(n) is the statement n^(2)-n+41 is prime. Prove that P(1),P(2) and P(3) are true. Prove also that P(41) is not true.

Let P(n) be the statement " n^2-n+41 " is prime. Prove that P(1), P(2) and P(3) are true. Also prove that P(41) is not true. How does this not contradict the Principle of Induction ?

Given that P(n, r)=n(n-1)(n-2) ….to r factors What are the values of P(n, 4) and P(n, 2)?

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