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📰 \sum_{k=1}^{50} \frac{1}{k(k+2)} = \frac{1}{2} \sum_{k=1}^{50} \left( \frac{1}{k} - \frac{1}{k+2} \right) 📰 \frac{1}{2} \left[ \left( \frac{1}{1} - \frac{1}{3} \right) + \left( \frac{1}{2} - \frac{1}{4} \right) + \left( \frac{1}{3} - \frac{1}{5} \right) + \cdots + \left( \frac{1}{50} - \frac{1}{52} \right) \right] 📰 Most terms cancel. The surviving positive terms are \(\frac{1}{1}, \frac{1}{2}\), and the surviving negative terms are \(-\frac{1}{51}, -\frac{1}{52}\) (since \(k+2 = 51, 52\) have no positive counterparts to cancel them). 📰 What Charstar Revealed Will Change How You Build Your Online Legend Forever 1907415 📰 Copy Infringement Revealed How One Viral Case Shook The Entire Industry Forever 716334 📰 Green Shoes That Hide More Than You Imagine Try Them Before Theyre Gone 5721698 📰 Sephora Shares 7228003 📰 Any Other Fibonacci Number Used Gives Fewer Groups 5200224 📰 Your Pc Needs Windows This Installer Tool Will Get It Up In Seconds 9841769 📰 Horns Up Find Out Exact Ps5 Release Date No One Spoke About Finally 9331840 📰 Watch This Usd To Cnh Swingits How Currency Traders Make Millions Every Second 1889336 📰 Kusakabe Unveiled The Hidden Trend Taking Over Japan In 2024 8127248 📰 Cebu Brooklyn New York 8473814 📰 Abby Phillip Salary 1968949 📰 Chat Gpt For Mac 6452935 📰 The Giant Leap For Gamers How Super Smash Bros Online Changed Online Fighting Forever 7915034 📰 Breakthrough Shock Department Of Health Unveils Massive New Employment Initiative 4871866 📰 5Vars Vaccine Hype Is Realthis Hidden Danger Could Change Everything You Know 8034108