Show that if the reward function (r) of a Markov decision problem is bounded in absolute value

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Show that if the reward function \(r\) of a Markov decision problem is bounded in absolute value by a constant \(c\), then for any policy \(\mathbf{u}\), the infinite horizon discounted value function of \(\mathbf{u}\) with discount factor \(\alpha\) is bounded in absolute value by \(c /(1-\alpha)\).

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