The series `2x/(x+30+(2x/(x+3)^2)+(2x/(x+3)^3)+……….to oo` will have a definite sum when (A) `-1ltxlt3` (B) `0ltxlt1` (C) `x=0` (D) none of these

The series . (2x)/(x + 3) + ((2x)/(x + 3))^(2) + ((2x)/(x + 3))^(3) + ...oo have a definite sum when

The series . (2x)/(x + 3) + ((2x)/(x + 3))^(2) + ((2x)/(x + 3))^(3) + ...oo have a definite sum when

Sum of the series 1+2^2x +3^2x^2 + 4^2x^3 …….to oo , |x| < 1 is :

The sum of the series 1 + 2x + 3x^(2) + 4x^(3) +"…." to oo where x lies between 0 and 1 i.e., 0 lt x lt 1 is :

The sum of the sereis 1+2^2x+3^2x^2+4^2x^3+…..oo where -1ltxlt1= (A) (1+x)/((1-x))^3 (B) x/((1+x)^3) (C) (1-x^2)/((1+x)^3) (D) none of these

The sum of the sereis 1+2^2x+3^2x^2+4^2x^3+…..oo where -1ltxlt1= (A) (1+x)/((1-x))^3 (B) x/((1+x)^3) (C) (1-x^2)/((1+x)^3) (D) none of these

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2) ,((x-1)^2, (x-2)^2, (x-3)^2), ((x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2),((x-1)^2 (x-2)^2, (x-3)^2), (x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2)) equals 0 (b) -1 (c) 1 (d) none of these