Infinite GP

Algebra Level 2

{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}

For a,b<1 |a|, |b| < 1 , define xx and yy as above. Find the value of

1+ab+a2b2+a3b3+.1+ab+a^2b^2+a^3b^3+\cdots.

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