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Question Number 89716 by abdomathmax last updated on 18/Apr/20
![calculate A_n =∫_0 ^∞ e^(−n[x]) sin((([x])/n))dx find nature of Σ n^2 A_n](Q89716.png)
$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{n}\left[{x}\right]} \:{sin}\left(\frac{\left[{x}\right]}{{n}}\right){dx} \\ $$$${find}\:{nature}\:{of}\:\Sigma\:{n}^{\mathrm{2}} \:{A}_{{n}} \\ $$