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Home » Step Into Warmth: The Ultimate Heated Jacket You Need This Winter! - Appcentric

Step Into Warmth: The Ultimate Heated Jacket You Need This Winter! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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rac{1}{k(k+2)} = rac{1}{2}\left( rac{1}{k} - rac{1}{k+2}
Now substitute into the sum:
\sum_{k=1}^{50} rac{1}{k(k+2)} = rac{1}{2} \sum_{k=1}^{50} \left( r...
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}...
The negative terms that do not cancel are $ -rac{1}{51}, -rac{1}{52}...

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