Given: $\lim_{x\rightarrow 1}\frac{x-1}{x^{n}-1}, x \in \mathbb{R}$

Because you cannot really get the limit with the current given function, I have used L'Hôpitals rule.

$f(x) = x-1$

$f'(x) = 1$

$g(x) = x^n-1$

$g'(x) = nx^{n-1}$

So we got:

$\lim_{x\rightarrow 1}\frac{1}{nx^{n-1}} = 0$ for $n>1$

What confuses me much is that I don't know anything about $n$. So can I just do it like that and define $n$ myself? If it is correct, would it be better if I'd write "for any large n" instead of $n>1$ ?

**Edit: The correct solution is $1/n$, not $0$!**