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

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

If log_(0.5)(x-2)ltlog_(0.25)(x-2)then x lies is the interval (A) (-3,-2) (B) (2,3) (C) (3,oo) (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

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 f(x)=(1-cos2x)/(x^(2)) , x!=0 and f(x) is continuous at x=0 ,then f(0)= (a) 1 (b) 2 (c) 3 (d) None of these

The sum of the coefficients in (1+x+3x^2)^2143 is (A) 2^2143 (B) 0 (C) 1 (D) -1

The sum of the series 1+2x+3x^(2)+4x^(3)+... upto infinity when x lies between 0 and 1 i.e.,0

The equation (x^(2)+x+1)^(2)+1=(x^(2)+x+1)(x^(2)-x-5) for x in(-2,3) will have number of solutions.1 b.2 c.3d.0