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Putnam 1941 B2

Source: Putnam 1941

February 23, 2022
PutnamConvergenceseries

Problem Statement

Find (i) lim⁡n→∞∑i=1n1n2+i2\lim_{n\to \infty} \sum_{i=1}^{n} \frac{1}{\sqrt{n^2 +i^{2}}}. (ii) lim⁡n→∞∑i=1n1n2+i\lim_{n\to \infty} \sum_{i=1}^{n} \frac{1}{\sqrt{n^2 +i}}. (iii) lim⁡n→∞∑i=1n21n2+i\lim_{n\to \infty} \sum_{i=1}^{n^{2}} \frac{1}{\sqrt{n^2 +i}}.
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