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

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

Find the sum of the series 1xx n+2(n-1)+3xx(n-2)+...+(n-1)xx2+n xx1

Find the sum of the series 1+3x+5x^(2)+7x^(3)+...... upto 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 series sum_(r=1)^(n)r.x^(r-1), using calculus.

If |x| lt 1 ,then the sum of the series 1 + 2x + 3x^(2) + 4x^(2) + ....infty will be

Find the sum to n terms of the series: 1+2x+3x^(2)+4x^(3)+......

Find the sum of the series tanx +2tan2x+2^2tan2^2 x+…=2^(n-1)tan2^(n-1)x

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