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Home » The Hidden Hack to Take Off Pressed Nails Fast—No More Stuckachen Stress! - Abbey Badges

The Hidden Hack to Take Off Pressed Nails Fast—No More Stuckachen Stress! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 P(2) = (2)^4 - 5(2)^3 + 6(2)^2 + 4(2) - 8

📌 = 16 - 5 \times 8 + 6 \times 4 + 8 - 8

📌 = 16 - 40 + 24 + 8 - 8

📌 = 16 - 40 + 24

📌 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:

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