Question

一道高二的题：求和-----------1+2x+3x^2+·····nx^(n-1)

Answer 1

设S=1+2x+3x^2+...nx^(n-1)

xS=x+2x^2+3x^3+.nx^n

xS-S=-1-x-x^2-.-x^(n-1)+nx^n

=-(x^n-1)/(x-1)+nx^n

S=nx^n/(x-1)-(x^n-1)/(x-1)^2