Tricky Infinite Sum

Calculus Level pending

\[6\left ( \frac{1}{2}+\frac{1}{2}\cdot\frac{0.5^{3}}{3}+\left ( \frac{1\cdot3}{2\cdot4} \right )\cdot\frac{0.5^{5}}{5}+\left ( \frac{1\cdot3\cdot5}{2\cdot4\cdot6} \right )\cdot\frac{0.5^{7}}{7}+\cdots \right ) = \, ? \]

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