Big O notation property Does the following correct and why?
$O(1)+O(\sqrt{n})=O(\sqrt{n})$,
where $O(.)$ means big O notation.
My thinking is that it is correct because
$\lim_{n \rightarrow\infty} \frac{1}{\sqrt{n}}=0 < \infty$. Thus  $1\leq \sqrt{n}$.

Your equation basically means a bounded function, say f, plus an another bounded function g times $\sqrt{n}$
so $\frac{f(n)+g(n)\sqrt{n}}{\sqrt{n}}$ is still bounded (as n tends to infinity), and yes, it's correct.
