Show that `n!(n+2)=n!+(n+1)!`

Let S_(n)=1+(1)/(2)+(1)/(3)+….+(1)/(n) Show that ns_(n)=n+((n-1)/(1)+(n-2)/(2)+………+(2)/(n-2)+(1)/(n-1)) .

If n is a natural number then show that n! + (n+1)! = (n+2)n!

Show that ((2n)!)/(n!) = 2^(n) { 1,3,5 ,…( 2n -1) }

Show that , (2n)! =2^(n).n![1.3.5…(2n-1)].

If y=ax^(n+1)+bx^(-n) then show that x^(2)y''=n(n+1)y .

Show that ((n+1)!)/((n-2)!)=n^(3)-n3

If y=x^(2)e^(x) ,show that y_(n)=(1)/(2)n(n-1)y_(2)-n(n-2)y_(1)+(1)/(2)(n-1)(n-2)}

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

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