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Question: Define $ M(v) = v - \frac{v^4}{4} $ for all real $ v $. If $ k $ is a positive integer, define $ b_k $ by
b_k = M\left( \frac{1}{k} \right) + M\left( \frac{2}{k} \right) + \cdots + M\left( \frac{k}{k} \right).
Find $ b_k $ in simplest form.

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