Find the sum of the series `1+3x+5x^2+7x^3+..........∞

Find the sum to ininity of the series 1-3x+5x^2+7x^3+..... oo when Ix| <1.

If x gt 0 then the sum of the series e^(-x) - e^(-2x) + e^(-3x) ......infty is

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

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 to infinity of the series 1^2+2^2x+3^2x^2+oodot

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 to n terms of each of the series in 3 × 1^(2) + 5 × 2^(2) + 7 × 3^(2) +.........

Find the sum of the squares of the roots of 3x^3-2x^2+4x+1=0

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

Find the sum of coefficients in (1+x-3x^2)^(4163)dot