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Find 1-(1)/(2)+(1)/(4)-(1)/(8)+(1)/(16)-...

Find `1-(1)/(2)+(1)/(4)-(1)/(8)+(1)/(16)-(1)/(32)+......oo`

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To solve the series \( S = 1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \frac{1}{16} - \frac{1}{32} + \ldots \), we can recognize that this series is an infinite geometric progression (GP). ### Step-by-Step Solution: 1. **Identify the first term (A) and the common ratio (R)**: - The first term \( A = 1 \). - The common ratio \( R \) can be found by dividing the second term by the first term: \[ ...
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