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

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

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

Prove the following by induction. 1 + r + r^2 +…..+ r^n = (r^(n+1) -1)/(r-1)

Prove the following by using the principle of mathematical induction for all n in N : a+a r+a r^2+...+a r^(n-1)=(a(r^n-1))/(r-1)

Prove :nPr=n(n-1)P(r-1)

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

Prove that: (i) ""^(n)P_(n)=""^(n)P_(n-1) " (ii) "^(n)P_(r)=n* ""^(n-1)P_(r-1) " (iii) "^(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)