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\( \sum_{k=2}^\infty \frac{1}{(k+5)(k+4)} \) \( = \sum_{k=2}^\infty ( \frac{1}{k+4} - \frac{1}{k+5} ) \) \( = \sum_{k=2}^\infty \frac{1}{k+4} - \sum_{k=2}^\infty \frac{1}{k+5} \) \( = \sum_{k=2}^\infty \frac{1}{k+4} - \sum_{k=3}^\infty \frac{1}{k+4} = \frac{1}{6} \)
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