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Home » The perimeter of the garden is calculated by the formula: - AMAZONAWS

The perimeter of the garden is calculated by the formula: - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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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:
All intermediate terms cancel, leaving:
- \frac{1}{51}
= \frac{51 - 1}{51} = \frac{50}{51}

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