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

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)+4*(n-3)+....(n−1).2+n.1" also, find the coefficient of x^(n-1) in th cxpansion of (1+2x+3x^(2)+"...."nx^(n-1))^(2) .

Find the sum of the series sum_(r=1)^(n)r xx r!

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

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

Find the sum of the series: 1xx2^(2)+2xx3^(2)+3xx4^(2)+... "to n terms"

Find the sum of the series: 1xx2^(2)+3xx3^(2)+5xx4^(2)+... "to n terms"

Find the sum of the series: (1)/((1xx3))+(1)/((3xx5))+(1)/((5xx7))+...+(1)/((2n-1)(2n+1))

Find the sum of the series: (1xx2xx4)+(2xx3xx7)+(3xx4xx10)+... "to n terms"

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