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1−(111)+(111×322)−(111×322×533)+⋯ 1 - \left(\dfrac1{11} \right) + \left ( \dfrac1{11} \times \dfrac3{22} \right) - \left( \dfrac1{11} \times \dfrac3{22} \times \dfrac5{33} \right) + \cdots 1−(111)+(111×223)−(111×223×335)+⋯
If the value of the series above is equal to ab \sqrt{\dfrac ab} ba, where aaa and bbb are coprime positive integers, find a+ba+ba+b.
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