# No idea about a single term?

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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