Let the first term of the geometric progression (GP) be \( a \) and the common ratio be \( r \). The sum of the first three terms is: a + ar + ar\(^2\) = a(1 + r + r\(^2\))

\(S_3 = a(1 + r + r^2)\)

The sum to infinity is:

\(S_{\infty} = \frac{a}{1 - r}\)

But: \(S_3 = \frac{1}{2} S_{\infty}\)

Substituting the expressions gives:

\(a(1 + r + r^2) = \frac{1}{2} \cdot \frac{a}{1 - r}\)

Dividing by \( a \):

\(1 + r + r^2 = \frac{1}{2(1 - r)}\)

Cross-multiplying:

\(2(1 + r + r^2)(1 - r) = 1\)

Expanding and simplifying leads to:

\(2(1 - r^3) = 1\)

Thus: \(r^3 = \frac{1}{2}\)

Taking the cube root:

\(r = \sqrt[3]{\frac{1}{2}} = \frac{1}{\sqrt[3]{2}}\)

Therefore, the positive common ratio of the progression is:

\(\frac{1}{\sqrt[3]{2}}\).