Question Number 34682 by math khazana by abdo last updated on 09/May/18 $${calculate}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:{ln}\left({cos}\left(\frac{{a}}{\mathrm{2}^{{n}} }\right)\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34679 by math khazana by abdo last updated on 09/May/18 $${let}\:{f}\left({x}\right)\:=\:\:\frac{{x}}{\mathrm{4}{x}^{\mathrm{2}} \:−\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{ontegr}\:{serie}\:. \\ $$ Terms of Service…
Question Number 34678 by math khazana by abdo last updated on 09/May/18 $${prove}\:{that}\:\forall\:{n}\geqslant\mathrm{3}\:\:\:\:\:\sqrt{{n}}\:\:<^{{n}} \sqrt{{n}!} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34676 by math khazana by abdo last updated on 09/May/18 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}−\mathrm{1}} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}+\mathrm{1}}\:=\sum_{{k}={n}+\mathrm{1}} ^{\mathrm{2}{n}} \:\:\frac{\mathrm{1}}{{k}} \\ $$ Terms of Service Privacy Policy…
Question Number 34677 by math khazana by abdo last updated on 09/May/18 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\left[{x}\:+\frac{{k}}{{n}}\right]\:=\left[{nx}\right]\:\:\forall\:{n}\in\:\in{N}^{\bigstar} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34672 by math khazana by abdo last updated on 09/May/18 $${prove}\:{that}\:\forall{n}\in{N}\:\:\:\mid{sin}\left({nx}\right)\mid\leqslant{n}\mid{sinx}\mid\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34666 by math khazana by abdo last updated on 09/May/18 $${simplify}\:{sin}^{\mathrm{2}} \left(\:\frac{{arccosx}}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34664 by math khazana by abdo last updated on 09/May/18 $${simplify} \\ $$$${g}\left({x}\right)=\:{arctan}\left(\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\right)\:−{arctan}\left(\frac{{x}}{{x}+\mathrm{1}}\right)\:+{arctan}\left(\frac{{x}−\mathrm{1}}{{x}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34665 by math khazana by abdo last updated on 09/May/18 $${simplify}\:\:{sin}\:\left(\mathrm{2}{arcsinx}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34663 by math khazana by abdo last updated on 09/May/18 $${simplify}\: \\ $$$${f}\left({x}\right)={arcsin}\left(\sqrt{\left.\mathrm{1}−{x}^{\mathrm{2}} \right)}\:\:−{arctan}\left(\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\right)\right. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com