Tính:
$\dfrac{\left(\dfrac{1+2^2+3^3+4^4+\ \!\!.\!.\!.+\ 2020^{2020}+ 2021^{2021}}{\dfrac{1}{20^3}+\dfrac{2}{30^4}+\dfrac{3}{40^5}+\dfrac{4}{50^6}+\ \!\!.\!.\!.+\ \dfrac{7025}{70260^{7027}}}\right)^{\large70275^{2021}}}{\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\dfrac{n^7}{3n^5}+\dfrac{3n^9}{5n^7}+\dfrac{5n^{11}}{7n^9}+\dfrac{7^{13}}{9^{11}}\ \!\!+\ \!\!.\!.\!.+\ \dfrac{1061n^{1067}}{1059n^{1065}}}\cdot \left(\dfrac{1783}{2}\cdot\dfrac{3^{3^2}-27^3}{7}\right)$
Xin đừng quan tâm đến những thứ thừa thãi trong bài toán này!
Ta có: A = $\dfrac{\left(\dfrac{1+2^2+3^3+4^4+\ \!\!.\!.\!.+\ 2020^{2020}+ 2021^{2021}}{\dfrac{1}{20^3}+\dfrac{2}{30^4}+\dfrac{3}{40^5}+\dfrac{4}{50^6}+\ \!\!.\!.\!.+\ \dfrac{7025}{70260^{7027}}}\right)^{\large70275^{2021}}}{\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\dfrac{n^7}{3n^5}+\dfrac{3n^9}{5n^7}+\dfrac{5n^{11}}{7n^9}+\dfrac{7^{13}}{9^{11}}\ \!\!+\ \!\!.\!.\!.+\ \dfrac{1061n^{1067}}{1059n^{1065}}}\cdot \left(\dfrac{1783}{2}\cdot\dfrac{3^{3^2}-27^3}{7}\right)$
⇒ A = $\dfrac{\left(\dfrac{1+2^2+3^3+4^4+\ \!\!.\!.\!.+\ 2020^{2020}+ 2021^{2021}}{\dfrac{1}{20^3}+\dfrac{2}{30^4}+\dfrac{3}{40^5}+\dfrac{4}{50^6}+\ \!\!.\!.\!.+\ \dfrac{7025}{70260^{7027}}}\right)^{\large70275^{2021}}}{\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\dfrac{n^7}{3n^5}+\dfrac{3n^9}{5n^7}+\dfrac{5n^{11}}{7n^9}+\dfrac{7^{13}}{9^{11}}\ \!\!+\ \!\!.\!.\!.+\ \dfrac{1061n^{1067}}{1059n^{1065}}}\cdot \left(\dfrac{1783}{2}\cdot\dfrac{0}{7}\right)$
⇒ A = $\dfrac{\left(\dfrac{1+2^2+3^3+4^4+\ \!\!.\!.\!.+\ 2020^{2020}+ 2021^{2021}}{\dfrac{1}{20^3}+\dfrac{2}{30^4}+\dfrac{3}{40^5}+\dfrac{4}{50^6}+\ \!\!.\!.\!.+\ \dfrac{7025}{70260^{7027}}}\right)^{\large70275^{2021}}}{\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\dfrac{n^7}{3n^5}+\dfrac{3n^9}{5n^7}+\dfrac{5n^{11}}{7n^9}+\dfrac{7^{13}}{9^{11}}\ \!\!+\ \!\!.\!.\!.+\ \dfrac{1061n^{1067}}{1059n^{1065}}} . 0$
⇒ A = 0
Vậy A = 0
`⇔ A = 0`
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`Lemonhuyg`