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Algebra Level 4

\[ \large \sum_{i=1}^{1000} (-1)^{i} \left( \dfrac { H_{i} + H_{i+1} }{ H_{i} - H_{i+1} } \right) \]

Consider the sequence \( H_{1}, H_{2} , \ldots , H_{n} \) where all \( H_{i} \) are in a harmonic progression. Then find the value of the summation above.

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