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Home » Prenez le logarithme naturel : \( \ln(0.2) = -0.1t \). - Nelissen Grade advocaten

Prenez le logarithme naturel : \( \ln(0.2) = -0.1t \). - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The sum becomes:

📌 \sum_{k=1}^{50} \left( \frac{1}{2k} - \frac{1}{k+1} + \frac{1}{2(k+2)} \right) = \frac{1}{2} \sum_{k=1}^{50} \frac{1}{k} - \sum_{k=1}^{50} \frac{1}{k+1} + \frac{1}{2} \sum_{k=1}^{50} \frac{1}{k+2}.

📌 Reindex the sums:

📌 = \frac{1}{2} \left( \sum_{k=1}^{50} \frac{1}{k} \right) - \left( \sum_{k=2}^{51} \frac{1}{k} \right) + \frac{1}{2} \left( \sum_{k=3}^{52} \frac{1}{k} \right).

📌 Combine terms:

📌 = \frac{1}{2} \left( 1 + \frac{1}{2} + \sum_{k=3}^{50} \frac{1}{k} \right) - \left( \frac{1}{2} + \sum_{k=3}^{50} \frac{1}{k} + \frac{1}{51} \right) + \frac{1}{2} \left( \sum_{k=3}^{50} \frac{1}{k} + \frac{1}{51} + \frac{1}{52} \right).

📌 = \frac{1}{2} + \frac{1}{4} - \frac{1}{2} - \frac{1}{51} + \frac{1}{2} \cdot \frac{1}{51} + \frac{1}{2} \cdot \frac{1}{52} = \frac{1}{4} - \frac{1}{102} + \frac{1}{104}.

📌 \frac{1}{4} - \frac{1}{102} + \frac{1}{104} = \frac{1}{4} - \frac{52 - 51}{5304} = \frac{1}{4} - \frac{1}{5304} = \frac{1326 - 1}{5304} = \frac{1325}{5304}.

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