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.

The product will have 102 zeroes since if you multiply any number like 1000,10, 10000, etc. then you just add zeroes to the end. If you multiplied a googol and 10 together, you add two more zeroes to the end of the number googol, making it have 102 zeroes.