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Home » ---Question: The average of $ 3v + 7 $, $ 5v - 4 $, and $ v + 10 $ is - Abu Waleed Tea

---Question: The average of $ 3v + 7 $, $ 5v - 4 $, and $ v + 10 $ is - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \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}

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