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n<= S_n <= Cn , where S_n= \frac{1}{\sqrt{j^2+k^2}}

Source: Austrian Polish 1982 APMC

April 30, 2020
inequalitiesminSumalgebra

Problem Statement

Define Sn=∑j,k=1n1j2+k2S_n=\sum_{j,k=1}^{n} \frac{1}{\sqrt{j^2+k^2}}. Find a positive constant CC such that the inequality n≤Sn≤Cnn\le S_n \le Cn holds for all n≥3n \ge 3. (Note. The smaller CC, the better the solution.)
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