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 , r)=P(n-1, r)+rdotP(n-1,\ r-1)

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

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

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

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0

If P(n ,4)=20 x P(n ,2),find n.

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

Find n if : P(2n, 3) = 100 P(n,2)

If P(n ,5): P(n ,3)=2:1 find n