MathNet 2026 — Part 03 Question 27

Find the sum of $1 \cdot 1! + 2 \cdot 2! + 3 \cdot 3! + \cdots + (n-1)(n-1)! + n \cdot n!$, where $n! = n(n-1)(n-2) \cdots 2 \cdot 1$.