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$\large \begin{cases} x=1+a+a^2+a^3+\cdots \\ y=1+b+b^2+b^3+\cdots \end{cases}$

For $|a|, |b| < 1$, define $x$ and $y$ as above. Find the value of

$1+ab+a^2b^2+a^3b^3+\cdots.$

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