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" 8.Prove that "^(n)P(n)=2^(n)P(n-2)...

" 8.Prove that "^(n)P_(n)=2^(n)P_(n-2)

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

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

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

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

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

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

Prove that: (i) (.^(n)P_(r))/(.^(n)P_(r-2)) = (n-r+1) (n-r+2)

Prove that 1* ""^(1)P_(1)+2* ""^(2)P_(2)+3* ""^(3)P_(3) + … +n* ""^(n)P_(n)=""^(n+1)P_(n+1)-1

Prove that ""^(2n+1)P_(n-1)=((2n+1)!)/((n+2)!) and ""^(2n-1)P_n=((2n-1)!)/((n-1)!)