What kind of Binomial is this?

Algebra Level 4

$1 + \frac {2}{3} \left ( \frac 1 2 \right )^1 + \frac {2 \times 5}{3 \times 6} \left ( \frac 1 2 \right )^2 + \frac {2 \times 5 \times 8}{3 \times 6 \times 9} \left ( \frac 1 2 \right )^3 + \cdots$

If the series above can be stated in the form $a^{1/b}$ for coprime positive integers $a$ and $b$, what is the value of $a+b?$

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