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Home » Question: Find the matrix $\mathbfM$ such that - Professionaloutdoormedia

Question: Find the matrix $\mathbfM$ such that - Professionaloutdoormedia

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 \boxed{\frac{3875}{5304}}

📌 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.

📌 M(v) = v - \frac{v^4}{4},

📌 b_k = \sum_{j=1}^{k} M\left( \frac{j}{k} \right) = \sum_{j=1}^{k} \left( \frac{j}{k} - \frac{1}{4} \left( \frac{j}{k} \right)^4 \right).

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