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$\large 1-\frac{1}{7}+\frac{1}{9}-\frac{1}{15}+\frac{1}{17} - \frac1{23} + \frac1{25} - \ldots = \ ?$

Clarification: Both $\{1,9,17,25,\ldots\}$ and $\{7,15,23,\ldots\}$ are arithmetic progressions.

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