1. n!(n+2)=n!+(n+1)! solve

n!(n+2) = n!+(n+1)! R.H.S = n!+(n+1)! = n!+(n+1)n! = n!(1+n+1) = n!(n+2) = L.H.S HENCE PROVED.

here we have  n![ n+2] = n! +[n+1]!

here we write [n+1]! as n!. [n+1]

n![n+2] =  n! + [n+1].n!

n!.[n+2] =  n![n+1+1]

n! [n+2] =  n![n+2]

here we obtain n+2 =n+2

so its true for all positive intezers 

you can check this by putting the values