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lim-n-k-1-n-k-2-2k-2-2nk-n-2-k-1-n-k-2-3k-2-3nk-n-2-1-n-




Question Number 154045 by EDWIN88 last updated on 14/Sep/21
 lim_(n→∞)  (((Σ_(k=1) ^n  (k^2 /(2k^2 −2nk+n^2 )))(Σ_(k=1) ^n  (k^2 /(3k^2 −3nk+n^2 )))))^(1/n)  =?
$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{{n}}]{\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{k}^{\mathrm{2}} }{\mathrm{2}{k}^{\mathrm{2}} −\mathrm{2}{nk}+{n}^{\mathrm{2}} }\right)\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{k}^{\mathrm{2}} }{\mathrm{3}{k}^{\mathrm{2}} −\mathrm{3}{nk}+{n}^{\mathrm{2}} }\right)}\:=? \\ $$
Commented by iloveisrael last updated on 15/Sep/21
 L=e^(−(π/(18))(9+4(√3) ))
$$\:{L}={e}^{−\frac{\pi}{\mathrm{18}}\left(\mathrm{9}+\mathrm{4}\sqrt{\mathrm{3}}\:\right)} \\ $$
Answered by Jonathanwaweh last updated on 14/Sep/21
is not possible
$${is}\:{not}\:{possible} \\ $$
Answered by rs4089 last updated on 14/Sep/21
1
$$\mathrm{1} \\ $$

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