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 e^(x-(1)/(2)(x -1)^(2) + (1)/(3) (x -1)^(3) - (1)/(4) (x -1)^(4) + ...

For x>0 the sum of the series (1)/(1+x)-(1-x)/((1+x)^(2))+((1-x)^(2))/((1+x)^(3))-...oo is equal to

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

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))

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

Find the sum of the series nC_(0)x^(3n)+(nC_(1))/(2)x^(3(n-1))(3-x^(3))+(nC_(2))/(3)x^(3(n-2))(3-x^(3))^(2)+......+(nC_(n))/(n+1)(3-x^(3))^(n)

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

Find the coefficient of x^(n) in the expansion of (1)/((1-x)(1-2x)(1-3x))

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

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