An algebra problem by Akshat Sharda

Algebra Level 3

If \(A_{1},A_{2},A_{3},\ldots\) is an arithmetic progression, then find the value of \(\displaystyle \sum^{2n}_{i=1}(-1)^{i}\left( \dfrac{A_{i}+A_{i+1}}{A_{i}-A_{i+1}}\right)\).

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