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Author: Tinku Tara

If-u-1-u-2-u-3-u-n-2n-2-n-is-a-AP-find-the-value-of-u-1-u-2-u-3-u-2n-2-u-2n-1-

Question Number 83406 by jagoll last updated on 02/Mar/20 $$\mathrm{If}\:\mathrm{u}_{\mathrm{1}} +\mathrm{u}_{\mathrm{2}} +\mathrm{u}_{\mathrm{3}} +…+\mathrm{u}_{\mathrm{n}} \:=\:\mathrm{2n}^{\mathrm{2}} +\mathrm{n}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\:\mathrm{AP}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{u}_{\mathrm{1}} +\mathrm{u}_{\mathrm{2}} +\mathrm{u}_{\mathrm{3}} +…+\mathrm{u}_{\mathrm{2n}−\mathrm{2}} +\mathrm{u}_{\mathrm{2n}−\mathrm{1}} \:. \\…

prove-that-2-3-2n-2-3-2n-is-an-even-integer-and-that-2-3-2n-2-3-2n-w-3-for-some-integers-w-for-all-integer-n-1-

Question Number 17867 by Mr easymsn last updated on 11/Jul/17 $${prove}\:{that}\:\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} +\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} {is}\:{an} \\ $$$${even}\:{integer}\:{and}\:{that}\:\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} −\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} ={w}\sqrt{\mathrm{3}} \\ $$$${for}\:{some}\:{integers}\:{w},{for}\:{all}\:{integer}\:{n}\geqslant\mathrm{1}. \\ $$$$ \\ $$ Answered by…

lim-x-6-8xsin-3-x-

Question Number 83401 by jagoll last updated on 02/Mar/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{6}−\mathrm{8xsin}\:\left(\frac{\mathrm{3}}{\mathrm{x}}\right)\right)=\:? \\ $$ Commented by mathmax by abdo last updated on 02/Mar/20 $$\mathrm{6}−\mathrm{8}{x}\:{sin}\left(\frac{\mathrm{3}}{{x}}\right)\sim\mathrm{6}−\mathrm{8}{x}×\frac{\mathrm{3}}{{x}}\:\Rightarrow{lim}_{{x}\rightarrow\infty} \left(\mathrm{6}−\mathrm{8}{x}\:{sin}\left(\frac{\mathrm{3}}{{x}}\right)\right)=\mathrm{6}−\mathrm{24}=−\mathrm{18} \\…