Sum Sn = x + 2x2 + 3x3 + +nxn(x≠0).

Sum Sn = x + 2x2 + 3x3 + +nxn(x≠0).


When x = 1, Sn = 1 + 2 + 3 + +When x ≠ 0 and X ≠ 1, Sn = x + 2x2 + 3x3 + +nxn,①xSn=x2+2x3+3x4+… +N xn + 1, and (1-x) Sn = x + x2 + X3 + +Xn-nxn + 1, so Sn = x (1 − xn) (1 − x) 2-nxn + 11 − X