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a-n-k-1-n-1-sin-2k-1-pi-2n-cos-2-k-1-pi-2n-cos-2-kpi-2n-find-lim-n-a-n-n-3-




Question Number 98557 by  M±th+et+s last updated on 14/Jun/20
a_n =Σ_(k=1 ) ^(n−1) ((sin((((2k−1)π)/(2n))))/(cos^2 ((((k−1)π)/(2n)))cos^2 (((kπ)/(2n)))))    find  lim_(n→∞) (a_n /n^3 )
$${a}_{{n}} =\underset{{k}=\mathrm{1}\:} {\overset{{n}−\mathrm{1}} {\sum}}\frac{{sin}\left(\frac{\left(\mathrm{2}{k}−\mathrm{1}\right)\pi}{\mathrm{2}{n}}\right)}{{cos}^{\mathrm{2}} \left(\frac{\left({k}−\mathrm{1}\right)\pi}{\mathrm{2}{n}}\right){cos}^{\mathrm{2}} \left(\frac{{k}\pi}{\mathrm{2}{n}}\right)} \\ $$$$ \\ $$$${find}\:\:\underset{{n}\rightarrow\infty} {{lim}}\frac{{a}_{{n}} }{{n}^{\mathrm{3}} } \\ $$

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