So we learned telescoping series in class and I came across this question in my textbook and I tried to evaluate it, but I don't understand how to do it.
$$ \sum\limits_{k=1}^n\left(k \cdot k!\right) $$
According to the answers:
$$ \sum\limits_{k=1}^n\left(k \cdot k!\right) = (n+1)! - 1 $$
We learned how to simplify certain telescoping series using partial fractions but I don't have any idea on how to start this question.