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Author: Tinku Tara

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} \\…

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Question Number 70780 by MJS last updated on 08/Oct/19 $$\frac{\mathrm{1}}{{t}+\sqrt{{u}}+\sqrt{{v}}}= \\ $$$$=\frac{\left({t}−\sqrt{{u}}+\sqrt{{v}}\right)\left({t}+\sqrt{{u}}−\sqrt{{v}}\right)\left({t}−\sqrt{{u}}−\sqrt{{v}}\right)}{\left({t}+\sqrt{{u}}+\sqrt{{v}}\right)\left({t}−\sqrt{{u}}+\sqrt{{v}}\right)\left({t}+\sqrt{{u}}−\sqrt{{v}}\right)\left({t}−\sqrt{{u}}−\sqrt{{v}}\right)}= \\ $$$$=\frac{{t}^{\mathrm{3}} −\left(\sqrt{{u}}+\sqrt{{v}}\right){t}^{\mathrm{2}} −\left(\sqrt{{u}}−\sqrt{{v}}\right)^{\mathrm{2}} {t}+\left({u}−{v}\right)\left(\sqrt{{u}}−\sqrt{{v}}\right)}{{t}^{\mathrm{4}} −\mathrm{2}\left({u}+{v}\right){t}^{\mathrm{2}} +\left({u}−{v}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\frac{\mathrm{1}}{{t}+\sqrt[{\mathrm{3}}]{{u}}+\sqrt[{\mathrm{3}}]{{v}}}= \\…

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}}…

find-the-domain-and-range-of-y-4x-2-3-x-lt-2-3x-1-x-2-

Question Number 5237 by sanusihammed last updated on 02/May/16 $${find}\:{the}\:{domain}\:{and}\:{range}\:{of}\: \\ $$$${y}\:=\:\left[_{\:\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:<\mathrm{2}} ^{\:\mathrm{3}{x}−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:\geqslant\:\mathrm{2}} \right. \\ $$ Answered by FilupSmith last updated on 02/May/16 $${Domain}\:=\:\left\{{x}:\:−\infty\leqslant{x}\leqslant\infty\right\}…

Find-the-range-and-domain-of-y-x-1-x-2-3x-10-x-2-6x-8-

Question Number 5235 by sanusihammed last updated on 02/May/16 $${Find}\:{the}\:{range}\:{and}\:{domain}\:{of}\: \\ $$$${y}\:=\:\frac{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{10}\right)}{{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{8}} \\ $$ Answered by Yozzii last updated on 02/May/16 $${x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{8}=\left({x}+\mathrm{3}\right)^{\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}\: \\…