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

Explanation

To find the sum of 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 series.

### Step 1: Identify the first term and common ratio
The first term \( a \) of the series is:
\[ a = 1 \]
The common ratio \( r \) can be determined by taking the ratio of the second term to the first term:
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