Question: Define $ M(v) = v - \frac{v^4}{4} $ for all real $ v $. If $ k $ is a positive integer, define $ b_k $ by
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- Find a common denominator for the subtracted terms:
- \frac{1}{51} + \frac{1}{52} = \frac{52 + 51}{51 \cdot 52} = \frac{103}{2652}.
- \boxed{\frac{3875}{5304}}
- 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.
- M(v) = v - \frac{v^4}{4},
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