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Home » Anderson Island Uncovered: The Hidden Paradise No One Talks About! 🌴🔥 - High Altitude Science

Anderson Island Uncovered: The Hidden Paradise No One Talks About! 🌴🔥 - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question:** A mathematician is analyzing a topological space and needs to compute the sum of the series \( \sum_{k=1}^{50} \frac{1}{k(k+1)} \) as part of a homology calculation. Calculate this sum.

📌 Solution:** The given series is \( \sum_{k=1}^{50} \frac{1}{k(k+1)} \). We can simplify the terms using partial fraction decomposition:

📌 \frac{1}{k(k+1)} = \frac{A}{k} + \frac{B}{k+1}

📌 Solving \( 1 = A(k+1) + Bk \), we equate coefficients:

📌 \( A + B = 0 \)

📌 \( A = 1 \)

📌 Thus, \( B = -1 \). So,

📌 The series becomes telescoping:

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