Category: Permutation and Combination

Question Number 146824 by alcohol last updated on 16/Jul/21 Answered by Olaf_Thorendsen last updated on 16/Jul/21 $$\mathrm{1}− \\ $$$${w}\:=\:{e}^{\frac{\mathrm{2}{i}\pi}{{n}}} \\ $$$$\mathrm{Let}\:{z}_{{n}} \:=\:\mathrm{1}+{w}+{w}^{\mathrm{2}} +…{w}^{{n}−\mathrm{1}} \\ $$$${z}_{{n}}…

Question Number 145863 by bramlexs22 last updated on 09/Jul/21 Answered by mr W last updated on 09/Jul/21 Commented by mr W last updated on 09/Jul/21…

Question Number 145104 by imjagoll last updated on 02/Jul/21 $$\:\mathrm{If}\:\frac{!\mathrm{6}}{\mathrm{x}}\:−!\mathrm{4}\:=\:!\mathrm{x}\:\mathrm{then}\:\mathrm{x}\:=? \\ $$ Answered by liberty last updated on 02/Jul/21 $$\:\Rightarrow\:\mathrm{265}−\mathrm{9}{x}\:=\:{x}.\left(!{x}\right) \\ $$$${test}\:{x}=\mathrm{5}\: \\ $$$$\Rightarrow\mathrm{265}−\mathrm{45}\:=\:\mathrm{220}\:\wedge\:\mathrm{5}.\left(!\mathrm{5}\right)=\mathrm{5}×\mathrm{44}=\mathrm{220} \\…

Question Number 79472 by jagoll last updated on 25/Jan/20 $$\mathrm{what}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{5}}\:+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{14x}+\mathrm{65}} \\ $$ Commented by john santu last updated on 25/Jan/20 $${yes}\:{sir}.\:{haha}\:{this}\:{method}\:{not}\:…

Question Number 78799 by Pratah last updated on 20/Jan/20 Commented by mathmax by abdo last updated on 20/Jan/20 $${convergence}?\:\:\:{let}\:{f}\left({x}\right)=\frac{{ln}\left({x}\right)}{{x}^{\frac{\mathrm{5}}{\mathrm{4}}} }\:\:\:{with}\:{x}\geqslant\mathrm{2}\:\:{we}\:{have} \\ $$$${f}^{'} \left({x}\right)=\frac{\frac{\mathrm{1}}{{x}}{x}^{\frac{\mathrm{5}}{\mathrm{4}}} −\frac{\mathrm{5}}{\mathrm{4}}{x}^{\frac{\mathrm{5}}{\mathrm{4}}−\mathrm{1}} {lnx}}{{x}^{\frac{\mathrm{5}}{\mathrm{2}}}…