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Home » Lowest power of 5: \( 5^1 \) - Veritas Home Health

Lowest power of 5: \( 5^1 \) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \frac{1}{2} \left( 1 + \frac{1}{2} - \frac{1}{51} - \frac{1}{52} \right).

📌 Compute the sum:

📌 \frac{1}{2} \left( \frac{3}{2} - \frac{1}{51} - \frac{1}{52} \right).

📌 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}}

📌 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).

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