Solution
= Solution
\b[True.] Rationalizing the <square root> gives, for $n\geq1$,
$$
0\leq\sqrt{n^2+n}-n=\frac n{\sqrt{n^2+n}+n}=\frac1{\sqrt{1+1/n}+1}\leq\frac12.
$$
The uniform bound is exactly the assertion $O(1)$ in <Big O notation>.
= Solution
\b[True.] Rationalizing the <square root> gives, for $n\geq1$,
$$
0\leq\sqrt{n^2+n}-n=\frac n{\sqrt{n^2+n}+n}=\frac1{\sqrt{1+1/n}+1}\leq\frac12.
$$
The uniform bound is exactly the assertion $O(1)$ in <Big O notation>.