Category: Arithmetic

Question Number 19330 by Tinkutara last updated on 09/Aug/17 $$\mathrm{A}\mathrm{triangle}\mathrm{with}\mathrm{perimeter}7\mathrm{has}\mathrm{integer}$$$$\mathrm{side}\mathrm{lengths}.\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{maximum}$$$$\mathrm{possible}\mathrm{area}\mathrm{of}\mathrm{such}\mathrm{a}\mathrm{triangle}?$$ Answered by mrW1 last updated on 09/Aug/17 $$\mathrm{3}/\mathrm{3}/\mathrm{1}\Rightarrow\mathrm{A}=\sqrt{\mathrm{3}.\mathrm{5}×\mathrm{0}.\mathrm{5}×\mathrm{0}.\mathrm{5}×\mathrm{2}.\mathrm{5}}=\mathrm{1}.\mathrm{479} \…

Question Number 84677 by jagoll last updated on 15/Mar/20 $$\underset{\mathrm{k}=1}{\sum ^{\mathrm{\infty }}}\frac{{\mathrm{k}}^2}{2^{\mathrm{k}}}?$$ Commented by Tony Lin last updated on 15/Mar/20 $$\frac{\mathrm{1}}{\mathrm{1}−{x}}=\mathrm{1}+{x}+{x}^{\mathrm{2}}…

Question Number 19053 by Tinkutara last updated on 03/Aug/17 $$\mathrm{Find}\mathrm{the}\mathrm{sum}:\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}$$$$-\frac{1}{7}+\frac{1}{8}-\frac{1}{9}+\dots$$ Answered by ajfour last updated on 03/Aug/17 $$\mathrm{ln}\:\left(\mathrm{1}+\mathrm{x}\right)=\mathrm{x}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{4}}+\frac{\mathrm{x}^{\mathrm{5}}…

Question Number 84532 by john santu last updated on 14/Mar/20 $$\mathrm{x}>0,\mathrm{y}>0\mathrm{prove}\mathrm{that}$$$$\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}<\mathrm{x}$$ Commented by mr W last updated on 14/Mar/20 $$\Rightarrow{y}<{x}+{y} \…

Question Number 84288 by jagoll last updated on 11/Mar/20 Commented by jagoll last updated on 11/Mar/20 $$\mathrm{dear}\mathrm{Mr}\mathrm{W}.\mathrm{please}\mathrm{help}\mathrm{me}$$ Commented by jagoll last updated on…