# How to simplify $\sum_{k=1}^nk\cdot k!$ [duplicate]

How do I go about simplifying this:

$$\sum_{k=1}^nk \cdot k!$$

Wolfram alpha tells me it's the same as $(n+1)!-1$ but I don't see how.

## marked as duplicate by Brian Borchers, Nosrati, KonKan, José Carlos Santos, Stefan4024Dec 1 '17 at 23:19

Hint: $$k\cdot k! = [(k+1)-1]\cdot k! = (k+1)!-k!$$