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Home » This Little Light of Mine Lyrics: The Secret? You Won’t Believe the Story! - inBeat

This Little Light of Mine Lyrics: The Secret? You Won’t Believe the Story! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Now substitute into the sum:

📌 \sum_{k=1}^{50} rac{1}{k(k+2)} = rac{1}{2} \sum_{k=1}^{50} \left( rac{1}{k} - rac{1}{k+2}

📌 This is a telescoping series. Write out the terms:

📌 rac{1}{2} \left[ \left( rac{1}{1} - rac{1}{3}

📌 ight) + \left( rac{1}{2} - rac{1}{4}

📌 ight) + \left( rac{1}{3} - rac{1}{5}

📌 ight) + \cdots + \left( rac{1}{50} - rac{1}{52}

📌 Most terms cancel. The positive terms that do not cancel are $ rac{1}{1}, rac{1}{2} $.

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