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lim-n-j-1-n-i-1-n-i-j-i-2-j-2-pi-2-ln-2-n-ln-n-




Question Number 175374 by MikeH last updated on 28/Aug/22
lim_(n→∞) (Σ_(j=1) ^n Σ_(i = 1) ^n ((i+j)/(i^2 +j^2 ))−((π/2)+ ln 2)n + ln n) = ?
$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\underset{{i}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\frac{{i}+{j}}{{i}^{\mathrm{2}} +{j}^{\mathrm{2}} }−\left(\frac{\pi}{\mathrm{2}}+\:\mathrm{ln}\:\mathrm{2}\right){n}\:+\:\mathrm{ln}\:{n}\right)\:=\:? \\ $$

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