FI-MO 2012 Problem 4

Let $k,n\in\mathbb{N},0<k<n.$ Prove that $\sum_{j=1}^k\binom{n}{j}=\binom{n}{1}+ \binom{n}{2}+\ldots + \binom{n}{k}\leq n^k.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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