Question Number 4822 by FilupSmith last updated on 16/Mar/16 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{mathematically}\:\mathrm{explain} \\ $$$$\mathrm{how}\:\mathrm{some}\:\mathrm{infinities}\:\mathrm{can}\:\mathrm{be}\:\mathrm{bigger}\:\mathrm{than} \\ $$$$\mathrm{others}?\:\mathrm{Thank}\:\mathrm{you}! \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 4781 by Dnilka228 last updated on 09/Mar/16 $$\frac{\sqrt{\delta{y}}}{\:\sqrt{\delta{x}}}×{f}_{\mathrm{1}} =\begin{vmatrix}{\delta{y}}\\{\delta{x}}\end{vmatrix}^{{x}/{z}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 4780 by Dnilka228 last updated on 09/Mar/16 $${D}_{\mathrm{1}} \rho=\mid\sqrt{{f}\left(\alpha+\beta\right)}×{c}^{\mathrm{2}} \mid \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 70312 by Shamim last updated on 03/Oct/19 $$\mathrm{If},\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{c}^{\mathrm{2}} }\:=\:\frac{\mathrm{1}}{\mathrm{ab}}+\frac{\mathrm{1}}{\mathrm{bc}}+\frac{\mathrm{1}}{\mathrm{ca}}\:\mathrm{then}\:\mathrm{prove}\: \\ $$$$\mathrm{that},\:\mathrm{a}=\mathrm{b}=\mathrm{c}. \\ $$ Commented by MJS last updated on 03/Oct/19 $$\mathrm{this}\:\mathrm{is}\:\mathrm{true}\:\mathrm{for}\:{a},\:{b},\:{c}\:\in\mathbb{R}…
Question Number 4775 by Yozzii last updated on 08/Mar/16 $${Let}\:\ast\:{be}\:{a}\:{binary}\:{operation}\:{on}\:\mathbb{Z} \\ $$$${defined}\:{by}\: \\ $$$${x}\ast{y}=\frac{\mathrm{1}}{\mathrm{2}}\left({x}+{y}+\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\left(−\mathrm{1}\right)^{{x}+{y}} \right)\right). \\ $$$${Is}\:\ast\:{associative}? \\ $$ Commented by prakash jain last updated…
Question Number 4751 by Yozzii last updated on 04/Mar/16 $${Find}\:{all}\:{functions}\:{h}:\mathbb{Z}\rightarrow\mathbb{Z}\:{such}\:{that} \\ $$$${h}\left({x}+{y}\right)+{h}\left({xy}\right)={h}\left({x}\right){h}\left({y}\right)+\mathrm{1} \\ $$$${for}\:{all}\:{x},{y}\in\mathbb{Z}. \\ $$ Commented by prakash jain last updated on 06/Mar/16 $${y}=\mathrm{0}…
Question Number 4748 by Yozzii last updated on 04/Mar/16 $${Find}\:{all}\:{real}\:\boldsymbol{{a}}\:{such}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)=\left\{\boldsymbol{{a}}{x}+{sinx}\right\}\: \\ $$$${is}\:{periodic}.\:\left\{{u}\right\}\:{is}\:{the}\:{fractional}−{part} \\ $$$${function}\:{of}\:{the}\:{real}\:{number}\:{u}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 4719 by prakash jain last updated on 29/Feb/16 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +…+{a}_{{n}} }{{n}}\leqslant\sqrt{\frac{{a}_{\mathrm{1}} ^{\mathrm{2}} +{a}_{\mathrm{2}} ^{\mathrm{2}} +…+{a}_{{n}} ^{\mathrm{2}} }{{n}}} \\ $$$$\mathrm{with}\:\mathrm{equality}\:\mathrm{holding}\:\mathrm{iff}\:{a}_{\mathrm{1}} ={a}_{\mathrm{2}}…
Question Number 4720 by prakash jain last updated on 29/Feb/16 $$\mathrm{Prove}\:\mathrm{or}\:\mathrm{counterexample}\:\mathrm{that}\:\mathrm{if}\:\mathrm{a}\:\mathrm{finite}\:\mathrm{number}\: \\ $$$$\mathrm{of}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{series}\:\mathrm{are}\:\mathrm{given}\:\mathrm{then}\:\mathrm{a}\:\mathrm{infinite}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{formulas}\:\mathrm{for}\:{n}^{{th}} \:\mathrm{term}\:\mathrm{exists}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{finite}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}. \\ $$$$\mathrm{For}\:\mathrm{example} \\ $$$$\mathrm{33},\mathrm{9},\mathrm{33},\mathrm{44},? \\ $$$$\mathrm{4}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{given}\:\mathrm{if}\:{a}_{{n}} ={f}\left({n}\right)\:\mathrm{then}\:\mathrm{there}\:\mathrm{are}…
Question Number 135786 by JulioCesar last updated on 16/Mar/21 Commented by Ar Brandon last updated on 16/Mar/21 $$\mathrm{You}\:\mathrm{mean}\: \\ $$$$\mathrm{H}=\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{9}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}} }}\:??? \\ $$…