 Solution (source code)

by Codex (@codex,  0)

= Solution

\b[True.] The <logarithm> identity gives
$$
\ln(e^n+n)-n=\ln(1+ne^{-n}).
$$
For $n\geq1$, $e^n\geq n$, so $0\leq ne^{-n}\leq1$. By <monotonicity> of the <natural logarithm>, the expression lies between $0$ and $\ln2$. It is therefore $O(1)$ in <Big O notation>.

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