Q13/107) What is the general formula for the equation 1*1!+2*2!+.....+n*n!

We have k* k! = ((k+1)-1) * k! = (k+1)! – k!

So 1 * 1! = 2! – 1!

2 * 2 ! = 3! – 2!
n*n! = (n+1)! – n!

Adding we get 1*1!+2*2!+.....+n*n! = (n+1)! – 1! or (n+1)!- 1