MathDB

9

Part of 1982 Austrian-Polish Competition

Problems(1)

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

Source: Austrian Polish 1982 APMC

4/30/2020
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.)
inequalitiesminSumalgebra