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Home » استخدم نظرية فيثاغورس: \(10^2 = 8^2 + \textالقاعدة^2\). - DNSFLEX

استخدم نظرية فيثاغورس: \(10^2 = 8^2 + \textالقاعدة^2\). - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\frac{1}{k(k+1)(k+2)} = \frac{1}{2k} - \frac{1}{k+1} + \frac{1}{2(k+2)...
The sum becomes:
\sum_{k=1}^{50} \left( \frac{1}{2k} - \frac{1}{k+1} + \frac{1}{2(k+2)}...
Reindex the sums:
= \frac{1}{2} \left( \sum_{k=1}^{50} \frac{1}{k} \right) - \left( \sum...
Combine terms:
= \frac{1}{2} \left( 1 + \frac{1}{2} + \sum_{k=3}^{50} \frac{1}{k} \ri...
= \frac{1}{2} + \frac{1}{4} - \frac{1}{2} - \frac{1}{51} + \frac{1}{2}...
\frac{1}{4} - \frac{1}{102} + \frac{1}{104} = \frac{1}{4} - \frac{52 -...
Final answer: $\boxed{\dfrac{1325}{5304}}$Question:

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