Question Number 93315 by Shakhzod last updated on 12/May/20 $${If}\:\:{n}>=\mathrm{2}\:\:{and}\:{n}\subset\mathbb{N}\:. \\ $$$${prove}\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+…\frac{\mathrm{1}}{{n}^{\mathrm{2}} }<={n}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\right)^{\frac{\mathrm{1}}{{n}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 93304 by Shakhzod last updated on 12/May/20 $$\int\sqrt{\mathrm{tan}\:\left({x}\right)}{dx}\:{Who}\:{can}\:{solve}\:{this}\:{problem}? \\ $$ Commented by john santu last updated on 12/May/20 $$=\:−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:}\mathrm{tanh}\:^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}+\sqrt{\mathrm{cot}\:\mathrm{x}}}{\:\sqrt{\mathrm{2}}}\right)\:+\: \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}−\sqrt{\mathrm{cot}\:\mathrm{x}}}{\:\sqrt{\mathrm{2}}}\right)+\mathrm{c}\:\:…
Question Number 158829 by MathsFan last updated on 09/Nov/21 $$\:{The}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\:\mathrm{2}{x}^{\mathrm{2}} +{px}+{q}=\mathrm{0}\:{are}\:\mathrm{2}\alpha+\beta\:{and} \\ $$$$\:\alpha+\mathrm{2}\beta.\:{Calculate}\:{the}\:{values}\:{of} \\ $$$$\:{p}\:{and}\:{q} \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 93284 by naka3546 last updated on 12/May/20 Commented by mr W last updated on 12/May/20 $${no}\:{unique}\:{solution}! \\ $$$$\left[{EFGH}\right]\geqslant\mathrm{2}\left[{ABCD}\right]=\mathrm{4}{M} \\ $$ Commented by mr…
Question Number 158794 by SANOGO last updated on 08/Nov/21 $${montrer}\:{que}\:\mathrm{7}\:{divise} \\ $$$$\mathrm{2222}^{\mathrm{5555}} +\mathrm{5555}^{\mathrm{2222}} \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated on 09/Nov/21 $${We}'{ll}\:\:{determine}\:{remainders}…
Question Number 27718 by mondodotto@gmail.com last updated on 13/Jan/18 Answered by prakash jain last updated on 13/Jan/18 $$\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\:\right)^{{x}} ={a} \\ $$$$\left(\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\:\right)^{{x}} =\frac{\mathrm{1}}{{a}} \\ $$$${a}+\frac{\mathrm{1}}{{a}}=\mathrm{4}\Rightarrow{a}^{\mathrm{2}} −\mathrm{4}{a}+\mathrm{1}=\mathrm{0}…
Question Number 158768 by EbrimaDanjo last updated on 08/Nov/21 $$ \\ $$$$\mathrm{evaluate} \\ $$$$\int\mathrm{2x}\sqrt{\mathrm{4x}−\mathrm{5}}\:\mathrm{dx} \\ $$ Answered by MJS_new last updated on 08/Nov/21 $$\int\mathrm{2}{x}\sqrt{\mathrm{4}{x}−\mathrm{5}}{dx}=? \\…
Question Number 93208 by Power last updated on 11/May/20 Commented by mathmax by abdo last updated on 11/May/20 $$\left.\mathrm{3}\right)\:{let}\:{s}\left({x}\right)\:=\sum_{{n}=\mathrm{0}} ^{\infty} \frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}{n}+\mathrm{1}}{x}^{\mathrm{2}{n}+\mathrm{1}} \:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${we}\:{have}\:{s}^{'}…
Question Number 93204 by liki last updated on 11/May/20 Commented by liki last updated on 11/May/20 $$…\mathrm{Q}\boldsymbol{\mathrm{n}}\:\mathrm{8}\:\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}},\mathrm{and}\:\mathrm{d} \\ $$ Answered by niroj last updated on…
Question Number 93203 by MAB last updated on 11/May/20 $${what}\:{is}\:{the}\:{average}\:{area}\:{of}\:{a}\:{triangle} \\ $$$${formed}\:{by}\:\mathrm{3}\:{random}\:{points}\:{in}\:{a}\:\mathrm{1}×\mathrm{1} \\ $$$${square}? \\ $$ Commented by prakash jain last updated on 11/May/20 https://math.stackexchange.com/questions/1236958/the-expected-area-of-a-triangle-formed-by-three-points-randomly-chosen-from-the…