Hello, I need some help with a proof by mathematical induction. Any help as soon as possible is appreciated

The equation is:

n

Σ k!.k = (n+1)! - 1

k=1

Now, here is what I have so far

n+1

Σ k! * k

k=1

goes to

n

Σ k! * k + (n+1)! * (n+1)

k=1

As for the right hand side, it becomes

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

=(n+2)! - 1

Now this is the point where i am stuck, how does

n

Σ k! * k + (n+1)! * (n+1)

k=1

become (n+2) -1 ?

or have I done something else wrong?