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📅 May 15, 2026 👤 scraface

May 15, 2026

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\sum_{n=1}^{50} \frac{1}{n(n+2)} = \frac{1}{2} \sum_{n=1}^{50} \left(...
This is a telescoping sum. Write out the first few terms:
\left( \frac{1}{1} - \frac{1}{3} \right) + \left( \frac{1}{2} - \frac{...
\frac{1}{2} \left( 1 + \frac{1}{2} - \frac{1}{51} - \frac{1}{52} \righ...
Compute the sum:
\frac{1}{2} \left( \frac{3}{2} - \frac{1}{51} - \frac{1}{52} \right).
Find a common denominator for the subtracted terms:
\frac{1}{51} + \frac{1}{52} = \frac{52 + 51}{51 \cdot 52} = \frac{103}...
\boxed{\frac{3875}{5304}}
Question: Define $ M(v) = v - \frac{v^4}{4} $ for all real $ v $. If $...

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