1.If ∣x∣<1|x| < 1∣x∣<1, ∣y∣<1|y| < 1∣y∣<1 and x≠1x \ne 1x=1, then the sum to infinity of the following series (x+y)+(x2+xy+y2)+(x3+x2y+xy2+y3)+⋯(x + y) + (x^2 + xy + y^2) + (x^3 + x^2 y + xy^2 + y^3) + \cdots(x+y)+(x2+xy+y2)+(x3+x2y+xy2+y3)+⋯ isa.x+y−xy(1+x)(1+y)\dfrac{x + y - xy}{(1 + x)(1 + y)}(1+x)(1+y)x+y−xyb.x+y+xy(1+x)(1+y)\dfrac{x + y + xy}{(1 + x)(1 + y)}(1+x)(1+y)x+y+xyc.x+y−xy(1−x)(1−y)\dfrac{x + y - xy}{(1 - x)(1 - y)}(1−x)(1−y)x+y−xyd.x+y+xy(1−x)(1−y)\dfrac{x + y + xy}{(1 - x)(1 - y)}(1−x)(1−y)x+y+xyLogin to continueOnly logged in users canattempt or see the solution.
