Question 126
Prove that, for all pairs of non-negative integers, $j, n$,
$$
\sum_{k=0}^{n} k^j \binom{n}{k} \ge 2^{n-jn}.
$$
$$
\sum_{k=0}^{n} k^j \binom{n}{k} \ge 2^{n-jn}.
$$
MathNet 2026 — Part 05 Question 126
Math Olympiad Vault · MathNet 2026 — Part 05