$\mathop {\lim }\limits_{x \to 1}\frac{x^n-1-n(x-1)}{(x-1)^2} = $
$\mathop {\lim }\limits_{x \to 1}\frac{(x-1)(x^{n-1}+x^{n-2}+...+x+1-n)}{(x-1)^2} = $
$\mathop {\lim }\limits_{x \to 1}\frac{x^{n-1}+x^{n-2}+...+x+1-n}{(x-1)} = $
$\mathop {\lim }\limits_{x \to 1}\frac{x^{n-1}-1+x^{n-2}-1+..+x-1}{(x-1)} = $
$\mathop {\lim }\limits_{x \to 1}\frac{x^{n-1}-1}{x-1}+\mathop {\lim }\limits_{x \to 1}\frac{x^{n-2}-1}{x-1}+...+\mathop {\lim }\limits_{x \to 1}\frac{x-1}{x-1}=$
$\mathop {\lim }\limits_{x \to 1}(x^{n-2}+x^{n-3}+....+x+1)+\mathop {\lim }\limits_{x \to 1}(x^{n-3}+x^{n-4}+....+x+1)+...+\mathop {\lim }\limits_{x \to 1}(1)=$
$(n-1)+(n-2)+...+2+1 = \frac{n(n-1)}{2}$
Làm đúng nhớ vote nhé, ủng hộ tinh thần