Which is larger?
\[\begin{align} A &= \dfrac1{2} + \dfrac1{2\times2} + \dfrac1{2\times2\times2} + \dfrac1{2\times2\times2\times2} + \cdots \\ \phantom0\\ B &= \dfrac0{2} + \dfrac1{2\times2} + \dfrac2{2\times2\times2} + \dfrac3{2\times2\times2\times2} + \cdots \end{align}\]
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