Giải thích các bước giải:
$\dfrac{S_n}{x}-S_n=1+x+x^2+..+x^{n-1}-nx^n$
$\to S_n(\dfrac{1}{x}-1)=(1+x+x^2+..+x^{n-1})-nx^n$
$\to S_n.\dfrac{1-x}{x}=\dfrac{x^n-1}{x-1}-nx^n$
$\to S_n.\dfrac{1-x}{x}=\dfrac{x^n-1-nx^n(x-1)}{x-1}$
$\to S_n.\dfrac{1-x}{x}=\dfrac{x^n-1-nx^{n+1}+nx^n}{x-1}$
$\to S_n.\dfrac{1-x}{x}=\dfrac{(1+n)x^n-1-nx^{n+1}}{x-1}$
$\to S_n.\dfrac{1-x}{x}=\dfrac{(1+n)x^n-nx^{n+1}-1}{x-1}$
$\to S_n.\dfrac{x-1}{x}=\dfrac{-(1+n)x^n+nx^{n+1}+1}{x-1}$
