If |`|a| lt 1 "and " |b| lt 1` then the sum of the series `1+(1+a)b+(1+a+a^2)b^2+(1+a+a^2+a^3)b^3+…..is `

If |a| lt 1 and |b| lt 1 then the sum of the series 1+(1+a) b+(1+a+ a^(2))b^(2)+ (1+a+a^(2)+a^(3)) b^(3)+cdots is

If |a| lt 1 and |b| lt 1 , then the sum of the series 1 + (1+a) b + (1 + a + a^(2))b^(2) + (1+ a+ a^(2) + a^(3))b^(3) … is

If |a|<1a n d|b|<1, then the sum of the series 1+(1+a)b+(1+a+a^2)b^2+(1+a+a^2+a^3)b^3+... is

If |a|<1and|b|<1, then the sum of the series 1+(1+a)b+(1+a+a^(2))b^(2)+(1+a+a^(2)+a^(3))b^(3)+ is (1)/((1-a)(1-b)) b.(1)/((1-a)(1-ab)) c.(1)/((1-b)(1-ab)) d.(1)/((1-a)(1-b)(1-ab))

If |a| < 1 and |b| < 1, then the sum of the series a(a+b)+a^2(a^2+b^2)+a^3(a^3+b^3)+.....oo is

If |a| < 1 and |b| < 1, then the sum of the series a(a+b)+a^2(a^2+b^2)+a^3(a^3+b^3)+.....oo is