$g(n)=n^a$, $f(n)=n^b$, where $a$ and $b$ are real numbers such that: $0 \lt a \lt b$.
I want to use L'Hopital's technique to prove that $g(n)$ belongs to $f(n)$.
My attempt: $ \lim_{n\to\infty}\frac{n^a}{n^{a+1}}.$
I'm using $a+1$ to state that $b \gt a$.
The problem is that I don't know if using $a+1$ is correct.