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find-lim-n-1-n-k-0-n-1-k-4n-2-k-2-




Question Number 107290 by mathmax by abdo last updated on 09/Aug/20
find lim_(n→+∞) (1/n)Σ_(k=0) ^(n−1)  (k/( (√(4n^2 −k^2 ))))
$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \frac{\mathrm{1}}{\mathrm{n}}\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}−\mathrm{1}} \:\frac{\mathrm{k}}{\:\sqrt{\mathrm{4n}^{\mathrm{2}} −\mathrm{k}^{\mathrm{2}} }} \\ $$

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