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If \( |x|<1,|y|<1 \) and \( x \neq y \), then the sum to infinity of the following series \( (x+y)+\left(x^{2}+x y…

Q1

If \( |x|<1,|y|<1 \) and \( x \neq y \), then the sum to infinity of the following series \( (x+y)+\left(x^{2}+x y+y^{2}\right)+ \) \( \left(x^{3}+x^{2} y+x y^{2}+y^{3}\right)+\ldots . . \) is :

a

\( \frac{x+y+x y}{(1+x)(1+y)} \)

b

\( \frac{x+y-x y}{(1-x)(1-y)} \)

c

\( \frac{x+y-x y}{(1+x)(1+y)} \)

d

\( \frac{x+y+x y}{(1-x)(1-y)} \)

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