Question

Prove that 1+1(1!)+2(2!)+....+n(n!) = (n+1)!

Answer 1

1(1!)=2!-1!

2(2!)=3!-2!
3(3!)=4!-3!
...............
...............

n(n!)=(n+1)!-n!

adding we get 
1(1!)+2(2!)+....+n(n!)=(n+1)!-1
hence
1+1(1!)+2(2!)+....+n(n!) = (n+1)!