The given series is a geometric series with the first term \(a = \frac{1}{2}\) and the common ratio \(r = -\frac{1}{2}\).

The formula for the sum of an infinite geometric series is:

\[S = \frac{a}{1 - r}\]

Plugging in the values \(a = \frac{1}{2}\) and \(r = -\frac{1}{2}\), we get:

\[S = \frac{\frac{1}{2}}{1 - \left(-\frac{1}{2}\right)} = \frac{\frac{1}{2}}{\frac{3}{2}} = \frac{1}{2} \cdot \frac{2}{3} = \frac{1}{3}\]

Now, subtracting 1 from the sum:

\[\frac{1}{3} - 1 = \frac{1 - 3}{3} = -\frac{2}{3}\]

Therefore, the value of the given expression is \(-\frac{2}{3}\).