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 1xx n+2(n-1)+3xx(n-2)+...+(n-1)xx2+n xx1

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 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 to n terms of the series n+(n-1)x+(n-2)x^(2)+.........+2x^(n-2)+x^(r)

find the sum of n terms: a(n) = n(n+1)-2

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

Find the sum of the series (1^(2)+1)1!+(2^(2)+1)2!+(3^(2)+1)3!+ . .+(n^(2)+1)n! .