Sum to n terms of the series `1+(1+x)+(1+x+x^2)+(1+x+x^2+x^3)+...`

Sum to n terms of the series (1)/((1 +x) (1 + 3x)) + (1)/( ( 1 + 3x) (1 + 5x)) + (1)/((1 + 5x ) (1 + 7x)) +…….

The sum of first n terms of the series 1 + (1 + x) y+ (1 + x + x^(2)) y^(2) + (1 + x + x^(2) + x^(3))y^(3) + ……….. is

Find the sum to n terms of the series : (x+1/x)^2+(x^2 + 1/x^2)^2+ (x^3 + 1/x^3)^2+ ...... .

The sum of n terms of the series (1)/(1 + x) + (2)/(1 + x^(2)) + (4)/(1 + x^(4)) + ……… is

The sum of n terms of the series (1)/(1 + x) + (2)/(1 + x^(2)) + (4)/(1 + x^(4)) + ……… is

Sum up to n terms the series 1+ 2x + 3x^(2) + 4x^(3) + ...

Sum to n terms of the series (1)/((1+x)(1+2x))+(1)/((1+2x)(1+3x))+(1)/((1+3x)(1+4x))+ ………

The sum of first n terms of the series 1+(1+x)y+(1+x+x^(2))y^(2)+(1+x+x^(2)+x^(3))y^(3)+.... is

Sum to n terms of the series (1)/((1+x)(1+2x))+(1)/((1+2x)(1+3x))+(1)/((1+3x)(1+4x))+ is (i) (1+x)(1+nx)((1+x)(1+nx))/((1+x)(1+(n-1)x))( iv )((1+x)(1+(n+1)x))/((1+x)(1+(n+1)x))