If `|x|<1a n d|y|<1,` find the sum of infinity of the following series: `(x+y)+(x^2+x y+y^2)+(x^3+x^2y+x y^2+y^3)+...................`

Explanation

To find the sum of the infinite series given by

\[ S = (x+y) + (x^2 + xy + y^2) + (x^3 + x^2y + xy^2 + y^3) + \ldots \]

where \( |x| < 1 \) and \( |y| < 1 \), we can follow these steps:

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