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show-that-lim-x-H-n-2F-1-1-1-2-1-ln-4-2ln-3-2F-1-1-1-2-1-2-

Question Number 80823 by M±th+et£s last updated on 06/Feb/20 $${show}\:{that}\: \\ $$$$\underset{{x}\rightarrow\infty} {{lim}}\:{H}_{{n}} =\mathrm{2}{F}_{\mathrm{1}} \left(\mathrm{1},\mathrm{1};\mathrm{2},\mathrm{1}\right) \\ $$$$ \\ $$$${ln}\left(\mathrm{4}\right)−\mathrm{2}{ln}\left(\mathrm{3}\right)=\mathrm{2}{F}_{\mathrm{1}} \left(\mathrm{1},\mathrm{1};\mathrm{2};\frac{−\mathrm{1}}{\mathrm{2}}\right) \\ $$ Answered by ~blr237~…

Question-15288

Question Number 15288 by ajfour last updated on 09/Jun/17 Commented by ajfour last updated on 09/Jun/17 $$\:{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{5}+\left[{x}\right]=\mathrm{0} \\ $$$$\Rightarrow\:\left({x}−\mathrm{3}\right)^{\mathrm{2}} =\mathrm{4}−\left[{x}\right]\:. \\ $$ Terms of…

Given-that-a-b-3-3-2-and-a-b-3-2-3-Find-i-ab-ii-a-2-b-2-

Question Number 146325 by 7770 last updated on 12/Jul/21 $${Given}\:{that}\:\left({a}+{b}\right)=\sqrt{\mathrm{3}\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}} \\ $$$${and}\:\left({a}−{b}\right)=\sqrt{\mathrm{3}\sqrt{\mathrm{2}}−\sqrt{\mathrm{3}}} \\ $$$${Find} \\ $$$$\left({i}\right)\:{ab}\:\:\:\:\:\:\left({ii}\right)\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} \\ $$ Answered by Ar Brandon last updated…

Question-15217

Question Number 15217 by Mr Chheang Chantria last updated on 08/Jun/17 Answered by ajfour last updated on 08/Jun/17 $$\:\:\:\boldsymbol{{v}}=\boldsymbol{{ab}}^{\mathrm{2}} +\boldsymbol{{a}}^{\mathrm{2}} \boldsymbol{{b}}+\boldsymbol{{ac}}+\boldsymbol{{bc}} \\ $$$$\:\:\:\boldsymbol{{v}}\:=\boldsymbol{{ab}}\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)+\boldsymbol{{c}}\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right) \\ $$$$\:\:\:\:\:\:=\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)\left(\boldsymbol{{ab}}+\boldsymbol{{c}}\right)\leqslant\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)\left[\frac{\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)^{\mathrm{2}}…