Question 116
Prove that
$$
-1 \lt \left( \sum_{k=1}^{n} \frac{k}{k^2 + 1} \right) - \ln n \le \frac{1}{2}, \quad n = 1, 2, \dots
$$
$$
-1 \lt \left( \sum_{k=1}^{n} \frac{k}{k^2 + 1} \right) - \ln n \le \frac{1}{2}, \quad n = 1, 2, \dots
$$
MathNet 2009-part-01 — 175 problems (EN–VI) Question 116
Math Olympiad Vault · MathNet 2009-part-01 — 175 problems (EN–VI)