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

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

If x is positive,the sum to infinity of the series (1)/(1+x)-(1-x)/((1+x)^(2))+((1-x)^(2))/((1+x)^(3))-((1-x)^(3))/((1+x)^(4))+is1/2 (b) 3/4 (c) 1 (d) none of these

intdx/((x-1)^(3/4)(x+2)^(5/4))= (A) 4/3((x-1)/(x+2))^(1/4)+c (B) 4/3sqrt((x-1)/(x+2))+c (C) 4/3((x+2)/(x-1))^(1/4)+c (D) none of these

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

Sum of the series 1+2^2x+3^2x^2+4^2x^3+.....to oo , |x| (A)    (1+x)/(1-x)^3    (B)    (1-x)/(1+x)^3     (C)    (2+x)/(1-x)^3    (D)    (1-x)/(1+x)^2

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

find 1+2^(2)x+3^(2)x^(2)+4^(2)x^(3)+......oo,|x|<1

For x>0 the sum of the series (1)/(1+x)-(1-x)/((1+x)^(2))+((1-x)^(2))/((1+x)^(3))-...oo is equal to

1+3x+6x^(2)+10x^(3)+.oo, where (x=(1)/(3)) is

x^((x-1)- 1/2 (x-1)^2+1/3((x-1)^3).- 1/4((x-1)^4).+…….. is equal to (A) 2logx (B) logx (C) x^2 (D) none of these