Question 150
Prove that
$$
1 \cdot 1! + 2 \cdot 2! + \cdots + n \cdot n! = (n+1)! - 1
$$
for all positive integers $n$.
$$
1 \cdot 1! + 2 \cdot 2! + \cdots + n \cdot n! = (n+1)! - 1
$$
for all positive integers $n$.
MathNet 2026 — Part 10 Question 150
Math Olympiad Vault · MathNet 2026 — Part 10