Sick-quences (7)

Probability Level 5

$1 - \left(\dfrac1{11} \right) + \left ( \dfrac1{11} \times \dfrac3{22} \right) - \left( \dfrac1{11} \times \dfrac3{22} \times \dfrac5{33} \right) + \cdots$

If the value of the series above is equal to $\sqrt{\dfrac ab}$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .