Find the sum of the series `1xxn+2(n-1)+3xx(n-2)+…+(n-1)xx2+nxx1`.

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

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: (1)/((1xx3))+(1)/((3xx5))+(1)/((5xx7))+...+(1)/((2n-1)(2n+1))

The sum of the series 1^(2) + 3^(2) + 5^(2) + ......+n'

Find the sum to n terms of each of the series in 1xx 2 xx 3 + 2 xx 3 xx 4 + 3 xx 4 xx 5 + ...

Find the sum to n terms of the series : 1xx2xx3 + 2xx3xx4 + 3xx4xx5 + dot dot dot

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

If P_(r) stands for ""^(r)P_(r) then the sum of the series 1+ P_(1 )+ ""2 xxP_(2) + ""3 xxP_(3) + … + ""n xxP_(n) is:

Find the sum to n terms of the series 1//(1xx2)+1//(2xx3)+1//(3xx4)++1//n(n+1)dot