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{x=1+a+a2+a3+⋯y=1+b+b2+b3+⋯\large \begin{cases} x=1+a+a^2+a^3+\cdots \\ y=1+b+b^2+b^3+\cdots \end{cases} ⎩⎨⎧x=1+a+a2+a3+⋯y=1+b+b2+b3+⋯
For ∣a∣,∣b∣<1 |a|, |b| < 1 ∣a∣,∣b∣<1, define xxx and yyy as above. Find the value of
1+ab+a2b2+a3b3+⋯ .1+ab+a^2b^2+a^3b^3+\cdots. 1+ab+a2b2+a3b3+⋯.
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