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📅 May 3, 2026 👤 scraface

May 03, 2026

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= 16 - 40 + 24 + 8 - 8
= 16 - 40 + 24
Question:** A mathematician is analyzing a topological space and needs...
Solution:** The given series is \( \sum_{k=1}^{50} \frac{1}{k(k+1)} \)...
\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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