I came across this question in some extracurricular problem sets my professor gave me: what is the closed form notation for the following sum:
$$S_n = 1\cdot1!+2\cdot2!+ ...+n \cdot n!$$
I tried computing some terms, and the only "vague" thing I noticed was that maybe I should be subtracting a term, but I'm really not sure. I went around looking on StackExchange's archives for a closed form of $S_n = 1!+2!+ ...+ n!$ but that didn't help me with my problem much.
Any pointers?