Question Number 146355 by bemath last updated on 13/Jul/21 $$\:\mathrm{If}\:\mathrm{3}^{\mathrm{4}^{\mathrm{2}^{{x}} } } =\:\mathrm{81}^{\mathrm{2}^{\mathrm{6}} } \:\mathrm{then}\:\sqrt{{x}^{\mathrm{2}} +\mathrm{5}}\:=? \\ $$ Answered by iloveisrael last updated on 13/Jul/21…
Question Number 80786 by M±th+et£s last updated on 06/Feb/20 Commented by mind is power last updated on 06/Feb/20 $${i}\:{will}\:{try}\:{not}\:{easy}\:! \\ $$ Commented by mr W…
Question Number 80708 by M±th+et£s last updated on 05/Feb/20 $${find}\:{sum}\:{of}\:{the}\:{series} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)} \\ $$ Commented by abdomathmax last updated on 05/Feb/20 $${S}=\sum_{{n}=\mathrm{0}}…
Question Number 146174 by ArielVyny last updated on 11/Jul/21 $${calculer}\:{lim}_{{x}\rightarrow\mathrm{1}} \left({x}−\mathrm{1}\right)\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{{n}^{{x}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 146157 by henderson last updated on 11/Jul/21 Answered by gsk2684 last updated on 11/Jul/21 $$\underset{\frac{\mathrm{1}}{{e}}} {\overset{\lambda} {\int}}\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{ln}\:{x}\right)\frac{{d}\left(\mathrm{1}−\mathrm{ln}\:{x}\right)}{−\mathrm{1}} \\ $$$$−\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{\left(\mathrm{1}−\mathrm{ln}\:{x}\right)^{\mathrm{2}} }{\mathrm{2}}\right]_{\frac{\mathrm{1}}{{e}}} ^{\lambda} \\ $$$$−\frac{\mathrm{1}}{\mathrm{4}}\left[\left(\mathrm{1}−\mathrm{ln}\:\lambda\right)^{\mathrm{2}}…
Question Number 146130 by Huy last updated on 11/Jul/21 $$\:\:\left(\mathrm{2}^{\mathrm{k}} +\mathrm{1}\right)\left(\mathrm{3}^{\mathrm{k}} +\mathrm{2}\right)\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{k}+\mathrm{5}\right) \\ $$$$\:\mathrm{min}\:\mathrm{k}=?\:\:\:\left(\mathrm{k}\in\mathbb{N}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 80559 by TawaTawa last updated on 04/Feb/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145982 by ArielVyny last updated on 10/Jul/21 $$\underset{{n}\geqslant\mathrm{0}} {\sum}\left(−\frac{\mathrm{1}}{\mathrm{81}}\right)^{{n}} \Gamma\left(\mathrm{3}{n}+\mathrm{3}\right)=?? \\ $$ Answered by Olaf_Thorendsen last updated on 10/Jul/21 $$\mathrm{diverges} \\ $$ Terms…
Question Number 145781 by Engr_Jidda last updated on 08/Jul/21 $${consider}\:{f}\left({x}\right)={Ax}^{\mathrm{2}} +{Bx}+{C} \\ $$$${with}\:{A}>\mathrm{0}.\:{Show}\:{that}\:{f}\left({x}\right)\geqslant\mathrm{0}\:\forall{x}\:\:{iff}\: \\ $$$${B}^{\mathrm{2}} −\mathrm{4}{AC}\leqslant\mathrm{0} \\ $$ Answered by ArielVyny last updated on 08/Jul/21…
Question Number 80230 by M±th+et£s last updated on 01/Feb/20 Answered by mind is power last updated on 03/Feb/20 $${let}\:{f}\left({z}\right)=\frac{\pi{cot}\left(\pi{z}\right)}{\mathrm{1}+{z}^{\mathrm{4}} },{Main}\:{idee}\:{use}\:{Residus}\:{Th} \\ $$$${and}\:{evaluate}\:{Integrales}\:{in}\:{Two}\:{ways} \\ $$$${pols}\:{of}\:{f}\:{are}\:\:\:{n}\in\mathbb{Z}\cup\left\{{e}^{{i}\left(\frac{\mathrm{1}+\mathrm{2}{k}}{\mathrm{4}}\right\}\pi} ,{k}\in\left\{\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3}\right\}\right\}…