Question 84
Prove for all integers $n \ge 0$ that
$$
\sum_{k=0}^{n} \frac{(n+k)!}{k!} = \frac{(2n+1)!}{(n+1)!}
$$
$$
\sum_{k=0}^{n} \frac{(n+k)!}{k!} = \frac{(2n+1)!}{(n+1)!}
$$
MathNet 2026 — Part 05 Question 84
Math Olympiad Vault · MathNet 2026 — Part 05