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

It is known that for x ne 1 , we have 1+x+x^(2)+….+x^(n-1)= (1-x^(n))/(1-x) , using this result, find the sum of the series 1+ 2x + 3x^(2)+…. +(n-1)x^(n-2) .

Find the sum of the series 1+3x+5x^(2)+7x^(2)+... to n terms.

Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

From the relation 1+x+x^(2)+* * * + x^(n-1)=(1-x^(n))/(1-x) , find the sum of the series 1+2x+3x^(2)+* * * +(n-1)x^(n-2) .

It is known for n ne 1 that : 1+x+x^2+..........+x^(n-1)=(1-x^(n))/(1-x) , hence find the sum of the series: 1+2x+3x^(2)+"….."+(n-1)x^(n-2) .

Find the sum of the series 1+3x+5x^(2)+7x^(3)+...... upto n terms.

Find the sum of the series 1+3x+5x^2+7x^3+...... n terms.

Find the sum of the series: 1.n+2.(n-1)+3.(n-2)+...+(n-1).2+n.1