Putnam 1941 B2

Find (i) $\lim_{n\to \infty} \sum_{i=1}^{n} \frac{1}{\sqrt{n^2 +i^{2}}}$ . (ii) $\lim_{n\to \infty} \sum_{i=1}^{n} \frac{1}{\sqrt{n^2 +i}}$ . (iii) $\lim_{n\to \infty} \sum_{i=1}^{n^{2}} \frac{1}{\sqrt{n^2 +i}}$ .