Find a closed form for

$$s_n = 1 \cdot 1! + 2 \cdot 2! + \ldots + n \cdot n! .$$
for integer $n \geq 1.$ your response should have a factorial.

In a singing competition, there are 150 participants. at the end of each round, 40% of the participants are eliminated. how many participants are left after n rounds?