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lim-n-k-1-n-j-1-n-2-sin-k-n-sin-k-n-2-1-n-2-j-ln-1-1-n-




Question Number 212311 by MrGaster last updated on 09/Oct/24
     lim_(n→∞)  Σ_(k=1) ^n   Σ_(j=1) ^n^2   sin(k/n)∙sin(k/n^2 )∙(1/( (√(n^2 +j))))ln(1+(1/n))
$$ \\ $$$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\:\underset{{j}=\mathrm{1}} {\overset{{n}^{\mathrm{2}} } {\sum}}\:\mathrm{sin}\frac{{k}}{{n}}\centerdot\mathrm{sin}\frac{{k}}{{n}^{\mathrm{2}} }\centerdot\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} +{j}}}\mathrm{l}{n}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right) \\ $$

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