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 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)+....... i s (a)1/2 (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

The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo will be a. x^n b. x^(-n) c. (1-1/x)^n d. none of these

(x)/(x+1)+(1)/(2)((x)/(x+1))^(2)+(1)/(3)((x)/(x+1))^(3)+....=

If (x)/((1+x^(2))(3-2x))=(A)/(3-2x)+(Bx+C)/(1+x^(2)) then C=

The sum of the series (x-1)/(x+1)+1/2(x^(2)-1)/(x+1)^(2)+1/3(x^(3)-1)/(x+1)^(3) +…is equal to

Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+....+n(1-x)(1-2x) (1-3x)............[1-(n-1)x].

2((2x)/(x^(2)+1)+(1)/(3)((2x)/(x^(2)+1))^(3) +(1)/(5)((2x)/(x^(2)+1))^(5)+…..oo)=