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5-4-9-2-9-16-25-3-13-36-49-4-17-64-81-5-21-100-121-

Question Number 70783 by naka3546 last updated on 08/Oct/19 $$\frac{\mathrm{5}}{\mathrm{4}\centerdot\mathrm{9}}\:+\:\mathrm{2}\left(\frac{\mathrm{9}}{\mathrm{16}\centerdot\mathrm{25}}\right)\:+\:\mathrm{3}\left(\frac{\mathrm{13}}{\mathrm{36}\centerdot\mathrm{49}}\right)\:+\:\mathrm{4}\left(\frac{\mathrm{17}}{\mathrm{64}\centerdot\mathrm{81}}\right)\:+\:\mathrm{5}\left(\frac{\mathrm{21}}{\mathrm{100}\centerdot\mathrm{121}}\right)\:+\:\ldots\:=\:\:? \\ $$ Commented by tw000001 last updated on 08/Oct/19 $$\mathrm{Well},\mathrm{this}\:\mathrm{one}\:\mathrm{is}\:\mathrm{unconverge}\:\mathrm{series}\:\mathrm{because} \\ $$$$\mathrm{difference}\:\mathrm{and}\:\mathrm{ratio}\:\mathrm{are}\:\mathrm{different}. \\ $$$$\mathrm{But}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{should}\:\mathrm{be}\:\mathrm{approximately} \\…

1-x-2-x-2-9-dx-

Question Number 136313 by aurpeyz last updated on 20/Mar/21 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}{dx} \\ $$ Answered by liberty last updated on 20/Mar/21 $$\int\:\frac{{dx}}{{x}^{\mathrm{3}} \:\sqrt{\mathrm{1}−\mathrm{9}{x}^{−\mathrm{2}} }}\:=\:\int\:\frac{{x}^{−\mathrm{3}} }{\:\sqrt{\mathrm{1}−\mathrm{9}{x}^{−\mathrm{2}}…

x-3-x-2-4-dx-

Question Number 136304 by aurpeyz last updated on 20/Mar/21 $$\int{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$ Answered by liberty last updated on 20/Mar/21 $$\:\int\:{x}^{\mathrm{2}} \:\left({x}\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:\right)\:{dx}\: \\…

x-3-x-2-9-dx-

Question Number 136301 by aurpeyz last updated on 20/Mar/21 $$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{9}}}{dx} \\ $$ Answered by liberty last updated on 20/Mar/21 $$\int\:{x}^{\mathrm{2}} \:\left(\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{9}}}\right){dx} \\…

If-x-3-1-x-3-1-compute-2-5-x-6-1-2-5-x-6-

Question Number 136303 by SOMEDAVONG last updated on 20/Mar/21 $$\mathrm{If}\:\mathrm{x}^{\mathrm{3}} −\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:\mathrm{1}\:.\mathrm{compute}\:\left(\mathrm{2}+\sqrt{\mathrm{5}}\right)\mathrm{x}^{\mathrm{6}} −\:\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{5}}\right)\mathrm{x}^{\mathrm{6}} }\:=\:? \\ $$ Answered by mr W last updated on 20/Mar/21 $${x}^{\mathrm{6}}…

I-cannot-understand-all-those-who-post-questions-like-x-x-2-cos-log-x-x-2pii-1-x-dx-and-a-few-minutes-later-5-3-2-1-9-4-I-mean-are-you-serious-

Question Number 70756 by MJS last updated on 07/Oct/19 $$\mathrm{I}\:\mathrm{cannot}\:\mathrm{understand}\:\mathrm{all}\:\mathrm{those}\:\mathrm{who}\:\mathrm{post} \\ $$$$\mathrm{questions}\:\mathrm{like}\:\int{x}^{\Gamma\left({x}^{\mathrm{2}} \right)} \mathrm{cos}\:\sqrt[{{x}}]{\mathrm{log}_{\varpi+{x}} \:{x}^{\mathrm{2}\pi\mathrm{i}} }{dx}=? \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathrm{few}\:\mathrm{minutes}\:\mathrm{later}\:\frac{\mathrm{5}}{\mathrm{3}}×\frac{\mathrm{2}+\mathrm{1}}{\mathrm{9}−\mathrm{4}}=? \\ $$$$\mathrm{I}\:\mathrm{mean},\:\mathrm{are}\:\mathrm{you}\:\mathrm{serious}? \\ $$ Commented by Rio…

lim-x-0-sinx-x-tanx-x-

Question Number 136243 by Khalmohmmad last updated on 19/Mar/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}{x}−{x}}{\mathrm{tan}{x}−{x}}=? \\ $$ Answered by EDWIN88 last updated on 20/Mar/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{x}}{\mathrm{tan}\:\mathrm{x}−\mathrm{x}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{x}−\mathrm{1}}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}} \\…