TITLE: Big oh of $(n+1)\sqrt{n-1}$
QUESTION [8 upvotes]: My instructor claims this is $O(n)$, but shouldn't it be $O(n^{1.5})$? If we ignore the $+1$ and $-1$ then this is just $O(n^{1.5})$. Is this reasoning right?
Any help is appreciated.

REPLY [2 votes]: More strongly, $(n + 1)\sqrt{n - 1} \sim n\sqrt{n};$ to wit, the limit of the ratio is 1.