The value of `(x-1)/(x+1)+(x^2-1)/(2(x+1)^2)+(x^3-1)/(3(x+1)^2) +......oo` equals

Sum of (x+(1)/(x))+(x^(2)+(1)/(x^(2)))+(x^(3)+(1)/(x^(3)))+.........oo is

If |x|lt(1)/(2), what is the value of 1+[(x)/(1-x)]+[(n(n+1))/(2!)][(x)/(1-x)]^(2)+............+oo ?

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

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

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

If x^(2)+x+1=0 then the absolute value of (x+(1)/(x))+(x^(2)+(1)/(x^(2)))+(x^(3)+(1)/(x^(3)))+...(x^(52)+(1)/(x^(52))) equals to

lim_(x rarr1)(x^((2)/(3))-2(x^((1)/(3))+1))/((x-1)^(2)) is equal to

The value of lim_(x to oo)((1+3x)/(2+3x))^((1-sqrt(x))/(1-x)) is

The value of lim_(x to oo)((1+3x)/(2+3x))^((1-sqrt(x))/(1-x)) is