" 10.Show that "n!(n+2)=n!+(n+1)!

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

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)) .

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

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

Show that If I _(n) =int cos ^(n) x dx, then show that I_(n) =1/n cos ^(n-1) x sin x + (n-1)/(n ) I_(n-2).

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

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 , (2n)! =2^(n).n![1.3.5…(2n-1)].