If $|x| < 1, |y| < 1$ and $x \neq 1$, then the sum to infinity of the following series $(x + y) + (x^{2} + xy + y^{2}) + (x^{3} + x^{2}y + xy^{2} + y^{3}) + \ldots$ is
(1) $\frac{x + y - xy}{(1 + x)(1 + y)}$
(2) $\frac{x + y + xy}{(1 + x)(1 + y)}$
(3) $\frac{x + y - xy}{(1 - x)(1 - y)}$
(4) $\frac{x + y + xy}{(1 - x)(1 - y)}$
If $|x| < 1, |y| < 1$ and $x \neq 1$, then the sum to infinity of the following series $(x + y) + (x^{2} + xy + y^{2}) + (x^{3} + x^{2}y + xy^{2} + y^{3}) + \ldots$ is\\
(1) $\frac{x + y - xy}{(1 + x)(1 + y)}$\\
(2) $\frac{x + y + xy}{(1 + x)(1 + y)}$\\
(3) $\frac{x + y - xy}{(1 - x)(1 - y)}$\\
(4) $\frac{x + y + xy}{(1 - x)(1 - y)}$