The sum of series `x/(1-x^2)+(x^2)/(1-x^4)+(x^4)/(1-x^8)+` to infinite terms, if `|x|<1,` is

Expand (1-x)^(1/3) upto 4 terms for |x|<1

The sum of series 1 + 2x + 3x^(2) + 4x^(3) + ...... up to infinity when x lies between 0 and 1 i.e., 0 lt x lt 1 is

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] .

Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiation.

If the sum to infinty of the series , 1+4x+7x^(2)+10x^(3)+…. , is (35)/(16) , where |x| lt 1 , then 'x' equals to

Simplify (4x)/(x^(2)-1)-(x+1)/(x-1)

Find the square root of (1+(2)/(x^(4))+(1)/(x^(8))) :