Question

Find a closed form for

Sn=1⋅1!+2⋅2!+…+n⋅n!.
for integer n≥1. Your response should have a factorial.

Answer 1

are you just looking to put it in sigma notation?

Answer 2

notice if you had 1+2+3+...+n
this can be written as
\[\sum_{i=1}^{n}i\]
notice if you had 1!+2!+3!+...+n!
this can be written as
\[\sum_{i=1}^{n}i!\]

Answer 3

anyways I hope this gives you an idea of how to write 1*1!+2*2!+...+n*n!
in sigma notation