Sử dụng cái này [TEX]a^n-1=(a-1)(a^{n-1}+a^{n-2}+.....+1)[/TEX]
Vậy [tex]lim\frac{x(x^{2017}-1)-2017(x-1)}{(x-1)^2}=lim\frac{x(x-1)(x^{2016}+..+1)-2017(x-1)}{(x-1)^2}=lim(\frac{(x-1)(x^{2017}+.+x-2017)}{(x-1)^2})=lim\frac{(x^{2017}-1)+(x^{2016}-1)+...+(x-1)}{(x-1)}=lim\frac{(x-1)[(x^{2016}+...+1)+(x^{2015}+...+1)+....+1]}{(x-1)}=2016+2015+...+1=\frac{2016.2017}{2}[/tex]
Sử dụng cái này [TEX]a^n-1=(a-1)(a^{n-1}+a^{n-2}+.....+1)[/TEX]
Vậy [tex]lim\frac{x(x^{2017}-1)-2017(x-1)}{(x-1)^2}=lim\frac{x(x-1)(x^{2016}+..+1)-2017(x-1)}{(x-1)^2}=lim(\frac{(x-1)(x^{2017}+.+x-2017)}{(x-1)^2})=lim\frac{(x^{2017}-1)+(x^{2016}-1)+...+(x-1)}{(x-1)}=lim\frac{(x-1)[(x^{2016}+...+1)+(x^{2015}+...+1)+....+1]}{(x-1)}=2016+2015+...+1=\frac{2016.2017}{2}[/tex]