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Home » Squadrons You Never Knew Existed (But Should Know About Right Now!) - 500apps

Squadrons You Never Knew Existed (But Should Know About Right Now!) - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📝 Recent Posts

\boxed{625}
Compute \(\sum_{k=1}^{50} \frac{1}{k(k+1)}\).
The given sum can be simplified using partial fraction decomposition:
\frac{1}{k(k+1)} = \frac{1}{k} - \frac{1}{k+1}
Thus, the sum becomes a telescoping series:
\sum_{k=1}^{50} \left( \frac{1}{k} - \frac{1}{k+1} \right)
Writing out the terms:
\left( \frac{1}{1} - \frac{1}{2} \right) + \left( \frac{1}{2} - \frac{...
Most terms cancel, leaving:
- \

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