Lim x--1 x^n - 1/ x- 1

Can i use induction therm .? If yas I have made it in this way

Lim x--1 x^n - 1/ x- 1
Lim x--1 (x-1)(x^(n-1)+ x^(n-2)+...+x+1)/(x-1)
Lim x--1 x^(n-1)+ x^(n-2)+...+x+1)

Then we notices that x^(n-1)+ x^(n-2)+...+x+1) Is equal to n then we can substitutes whit n and we get
Lim x--1 (n)

Question

Lim x-->1 x^n - 1/ x- 1 

Can i  use induction therm .? If yas I have made it in this way 

Lim x-->1 x^n - 1/ x- 1 
Lim x-->1 (x-1)(x^(n-1)+ x^(n-2)+...+x+1)/(x-1) 
Lim x-->1 x^(n-1)+ x^(n-2)+...+x+1)

Then we notices that  x^(n-1)+ x^(n-2)+...+x+1) Is equal to n then we can substitutes whit n  and we get 
Lim x-->1 (n)

myininaya · Answer

n is correct
$$\lim_{x \rightarrow 1}\frac{x^n-1}{x-1}=n$$