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Home » You Wont Believe How EASY It Is to Delete Your Microsoft Account Forever! - Moon Smoking

You Wont Believe How EASY It Is to Delete Your Microsoft Account Forever! - Moon Smoking

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 \frac{1}{k(k+1)(k+2)} = \frac{1}{2k} - \frac{1}{k+1} + \frac{1}{2(k+2)}.

📌 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}.

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