Math Problem Statement
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Solution
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Math Problem Analysis
Mathematical Concepts
Series Convergence
Partial Fraction Decomposition
Telescoping Series
Formulas
\( \sum_{k=1}^{\infty} \frac{1}{(k+2)(k+3)} \)
Partial fraction: \( \frac{1}{(k+2)(k+3)} = \frac{1}{3} \left( \frac{1}{k+2} - \frac{1}{k+3} \right) \)
Theorems
Telescoping Series
Suitable Grade Level
Grades 11-12 or early university level
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