Question Number 57434 by Tawa1 last updated on 04/Apr/19 $$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{way}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{infinity}\:\mathrm{of}\:\mathrm{a}\:\mathrm{product}\:\mathrm{operator} \\ $$$$\:\:\mathrm{e}.\mathrm{g}\:\:\:\:\:\mathrm{product}\:\mathrm{of}\:\:\:\:\:\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}.\mathrm{5}\:…\:\:\left[\mathrm{1},\:\mathrm{infinity}\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 122957 by I want to learn more last updated on 21/Nov/20 Commented by mr W last updated on 21/Nov/20 $${see}\:{Q}\mathrm{74970} \\ $$ Answered…
Question Number 122950 by bemath last updated on 21/Nov/20 $$\:\:\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{3}+…\sqrt{\mathrm{1}+\mathrm{2014}+\sqrt{\mathrm{1}+\mathrm{2015}.\mathrm{2016}}}}}}\:=\:? \\ $$ Commented by Dwaipayan Shikari last updated on 21/Nov/20 $$\mathrm{2} \\ $$$$\sqrt{\mathrm{1}+\mathrm{2}+\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{…}}}}=\mathrm{3} \\ $$$$\sqrt{\mathrm{1}+\mathrm{3}}=\mathrm{2}…
Question Number 188482 by mathlove last updated on 02/Mar/23 $$\mathrm{512}{x}^{\mathrm{1}−{x}^{−\mathrm{3}} } =−\mathrm{1} \\ $$$${find}\:\:{volue}\:\:{of}\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left({x}^{\mathrm{2}} \right)^{{n}} =? \\ $$ Answered by mr W last…
Question Number 122897 by Study last updated on 20/Nov/20 Answered by Dwaipayan Shikari last updated on 20/Nov/20 $$\mathrm{9}+\mathrm{9}+\mathrm{15}×\mathrm{3}=\mathrm{63} \\ $$$${or} \\ $$$$\mathrm{9}+\mathrm{9}+\mathrm{15}^{\mathrm{3}} =\mathrm{3383} \\ $$$${Many}\:{more}\:{possibilities}..…
Question Number 188430 by mnjuly1970 last updated on 01/Mar/23 $$ \\ $$$$\:\:\:\:\mathrm{2}\lfloor\:{x}\:\rfloor\:−\:\lfloor\:−{x}\:\rfloor\:=\mathrm{4} \\ $$$$\:\:\:−−−− \\ $$$$\:\:{if}\:\:{x}\in\mathbb{Z}\:\Rightarrow\:\:\mathrm{2}{x}\:+{x}\:=\:\mathrm{4}\:\Rightarrow\:{x}=\frac{\mathrm{4}}{\mathrm{3}}\:\:,{impossible} \\ $$$$\:\:{if}\:{x}\notin\:\mathbb{Z}\:\overset{\lfloor−{x}\rfloor=−\lfloor{x}\rfloor−\mathrm{1}} {\Rightarrow}\mathrm{2}\lfloor{x}\rfloor+\lfloor{x}\rfloor=\mathrm{3} \\ $$$$\:\:\:\:\:\Rightarrow\:\lfloor\:{x}\:\rfloor=\:\mathrm{1}\:\Rightarrow\:\:\mathrm{1}\leqslant\:{x}\:<\:\mathrm{2}\:\:\:\:\overset{{x}\neq\mathrm{1}} {\Rightarrow}\:{x}\in\:\left(\mathrm{1}\:,\:\mathrm{2}\right)\:\:\:\checkmark \\ $$$$ \\…
Question Number 122883 by kolos last updated on 20/Nov/20 $$\sum_{\mathrm{1}} ^{\infty} \left(\frac{\mathrm{sin}\:\left(\mathrm{x}\right)}{\mathrm{x}}\right)=? \\ $$ Commented by Dwaipayan Shikari last updated on 20/Nov/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sinx}}{{x}}=\frac{\mathrm{1}}{\mathrm{2}{i}}\underset{{n}=\mathrm{1}}…
Question Number 188407 by HeferH last updated on 01/Mar/23 $${xf}\left({x}\right)\:=\:{f}\left({x}\:+\:\mathrm{2}\right) \\ $$$${f}\left(\mathrm{2}\right)\:=\:\mathrm{2} \\ $$$${f}\left(\mathrm{8}\right)\:=\:?\: \\ $$ Answered by horsebrand11 last updated on 01/Mar/23 $$\left({i}\right)\:{x}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right) \\…
Question Number 57328 by ANTARES VY last updated on 02/Apr/19 Answered by mr W last updated on 02/Apr/19 $${let}\:\alpha=\frac{\angle{A}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\alpha=\frac{{r}}{{AO}}=\frac{\mathrm{2}×\mathrm{3}}{\mathrm{10}}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$\Rightarrow\mathrm{tan}\:\alpha=\frac{\mathrm{3}}{\:\sqrt{\mathrm{5}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }}=\frac{\mathrm{3}}{\mathrm{4}}…
Question Number 122860 by greg_ed last updated on 20/Nov/20 Answered by MJS_new last updated on 20/Nov/20 $$\mathrm{both}\:\mathrm{sides}\:\geqslant\mathrm{0}\:\Rightarrow\:\mathrm{squaring}\:\mathrm{allowed} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}\mid{xy}\mid\leqslant\mathrm{2}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)+\mathrm{2}\mid{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \mid…