\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f : \mathbb{R} \to \mathbb{R}\) be convex. Show that the sequence \((u_n)_{n \in \mathbb{N}}\) defined by \(u_n = f(n+1) - f(n)\) is nondecreasing.
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