Matematické Fórum

stuart clark · 03. 09. 2019 11:38

Evaluation of $\lim_{n\rightarrow \infty}\lim_{m\rightarrow \infty}\sum^{n}_{r=1}\sum^{mr}_{k=1}\frac{m^2n^2}{(m^2n^2+k^2)(n^2+r^2)}$

laszky · 29. 10. 2019 23:44 — Editoval laszky (29. 10. 2019 23:44)

↑ stuart clark:

Hi, the worst estimate here gives

$\sum^{n}_{r=1}\sum^{mr}_{k=1}\frac{m^2n^2}{(m^2n^2+k^2)(n^2+r^2)} \geq \sum^{n}_{r=1}\sum^{mr}_{k=1}\frac{m^2n^2}{(m^2n^2+m^2n^2)(n^2+n^2)} = \sum^{n}_{r=1}\sum^{mr}_{k=1}\frac{1}{4n^2} =$
$= \sum^{n}_{r=1} \frac{mr}{4n^2} = \frac{mn(n+1)}{8n^2} = \frac{m}{8} + \frac{m}{8n} \stackrel{m\to\infty}{\longrightarrow}+\infty$

stuart clark · 31. 10. 2019 11:20

Thanks ↑ laszky:

Matematické Fórum

#1 03. 09. 2019 11:38

Double summation

#2 29. 10. 2019 23:44 — Editoval laszky (29. 10. 2019 23:44)

Re: Double summation

#3 31. 10. 2019 11:20

Re: Double summation

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