題組內容

3. Let $f(x) = \frac{1}{1 + x^2}$, $0 \leq x \leq 1$ and $P = \{0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1\}$ be a partition of $[0, 1]$.

(c) (7%) Evaluate \( \lim_{n\to \infty}\left[\sum_{i=1}^{n}\frac{n}{n^2 + i^2}\right] \).