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

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

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