$\lim_{n \to \infty} \sum_{r=0}^{n-1} \frac{n}{n^2 + r^2}$ equals:
Step-by-Step Solution
Key Concept: Write the general term as $\frac{1}{n} \cdot \frac{1}{1 + (r/n)^2}$ and recognise the sum as a Riemann sum that converges to a definite integral over $[0, 1]$.
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Correct Answer: (1)