Question Number 151268 by rs4089 last updated on 19/Aug/21 $$\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} }{{r}}\left[\psi\left(\frac{{r}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}\right)−\psi\left(\frac{{r}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{4}}\right)\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20198 by Joel577 last updated on 24/Aug/17 $$\mathrm{Find}\:\mathrm{exact}\:\mathrm{form}\:\mathrm{of} \\ $$$$\mathrm{cos}\:\left(\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\right) \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}}\right)…
Question Number 151265 by liberty last updated on 19/Aug/21 Commented by Tawa11 last updated on 19/Aug/21 $$\mathrm{Weldone}\:\mathrm{sir}. \\ $$ Commented by liberty last updated on…
Question Number 20195 by mondodotto@gmail.com last updated on 23/Aug/17 Answered by Tinkutara last updated on 23/Aug/17 $$\mathrm{Let}\:{x}\:=\:\mathrm{2}^{{y}} \\ $$$$\mathrm{2}^{{y}\left({y}+\mathrm{4}\right)} \:=\:\mathrm{2}^{\mathrm{5}} \\ $$$${y}^{\mathrm{2}} \:+\:\mathrm{4}{y}\:−\:\mathrm{5}\:=\:\mathrm{0} \\ $$$$\left({y}\:+\:\mathrm{5}\right)\left({y}\:−\:\mathrm{1}\right)\:=\:\mathrm{0}…
Question Number 20194 by ajfour last updated on 23/Aug/17 $${A}\:{plane}\:{is}\:{drawn}\:{through}\:{the}\: \\ $$$${midpoint}\:{of}\:{a}\:{diagonal}\:{of}\:{a}\:{cube} \\ $$$${perpendicular}\:{to}\:{the}\:{diagonal}. \\ $$$${Determine}\:{the}\:{area}\:{of}\:{the}\:{figure} \\ $$$${resulting}\:{from}\:{the}\:{section}\:{of}\:{the} \\ $$$${cube}\:{cut}\:{by}\:{this}\:{plane}\:{if}\:{the}\:{edge} \\ $$$${of}\:{the}\:{cube}\:{is}\:{equal}\:{to}\:\boldsymbol{{a}}. \\ $$ Commented…
Question Number 85729 by jagoll last updated on 24/Mar/20 $$\mathrm{if}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2020}\:\mathrm{is}\:\mathrm{Tuesday}, \\ $$$$\mathrm{then}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2032}\:\mathrm{is}\:\mathrm{the}\:\mathrm{day}\:? \\ $$ Commented by jagoll last updated on 24/Mar/20 $$\mathrm{what}\:\mathrm{the}\:\mathrm{simple}\:\mathrm{method} \\ $$$$\mathrm{for}\:\mathrm{calculate}\:\mathrm{it}? \\…
Question Number 20192 by naziri1920@gmail.com last updated on 23/Aug/17 $$ \\ $$$${t}_{\mathrm{1}} =\mathrm{3},\:{t}_{{n}} =\mathrm{3}{t}_{{n}−\mathrm{1}} +\mathrm{2}\:\:\:\:\:….{n}>\mathrm{1} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$…
Question Number 20187 by naziri1920@gmail.com last updated on 23/Aug/17 $${t}_{{n}} =\frac{{t}_{{n}−\mathrm{1}} }{{n}^{\mathrm{2}} },\:{t}_{\mathrm{1}} =\mathrm{3};{t}_{\mathrm{2}} ,{t}_{\mathrm{3}} ,\left({n}\geqslant\mathrm{2}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\…
Question Number 151256 by pticantor last updated on 19/Aug/21 $$\:{A}_{{n}} =\mathrm{2}^{{n}} +\mathrm{3}^{{n}} +\mathrm{4}^{{n}} +\mathrm{5}^{{n}} \\ $$$${B}_{{n}} =\mathrm{100}^{{n}} +\mathrm{101}^{{n}} +\mathrm{102}^{{n}} +\mathrm{103}^{{n}} \\ $$$$\left.\mathrm{1}\right)\boldsymbol{{find}}\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\boldsymbol{{n}}\:\boldsymbol{{while}}\:\mathrm{7}\mid\boldsymbol{{A}}_{\boldsymbol{{n}}} \\ $$$$\left.\mathrm{2}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{B}}_{\boldsymbol{{n}}} \equiv\boldsymbol{{A}}_{\boldsymbol{{n}}}…
Question Number 85721 by M±th+et£s last updated on 24/Mar/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}} {ln}\left({x}\right)}{\:\sqrt{{x}}}{dx}=−\sqrt{\pi}\left(\gamma+{ln}\left(\mathrm{4}\right)\right) \\ $$ Answered by mind is power last updated on…