Sick-quences (7)

Discrete Mathematics 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 \(a+b\).