Question Number 34688 by math khazana by abdo last updated on 09/May/18 $${cslculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:{ln}\left(\mathrm{1}+\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}\right) \\ $$ Commented by abdo mathsup 649 cc last…
Question Number 34689 by math khazana by abdo last updated on 09/May/18 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:=\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{2}{n}}\:+{o}\left(\frac{\mathrm{1}}{{n}}\right) \\ $$ Commented by abdo mathsup 649 cc last…
Question Number 34690 by math khazana by abdo last updated on 09/May/18 $${let}\:{U}_{{n}} =\frac{\mathrm{1}}{{n}!}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left({arcsinx}\right)^{{n}} {dx} \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \:. \\ $$ Terms of…
Question Number 34687 by math khazana by abdo last updated on 09/May/18 $${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\left(\frac{\mathrm{1}}{\:\sqrt{{n}−\mathrm{1}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{{n}+\mathrm{1}}}\:−\frac{\mathrm{2}}{\:\sqrt{{n}}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34683 by math khazana by abdo last updated on 09/May/18 $${find}?{the}\:{nature}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{sin}\left\{\pi\left(\mathrm{2}+\sqrt{\mathrm{3}}\:\right)^{{n}} \right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34684 by math khazana by abdo last updated on 09/May/18 $${let}\:{U}_{{n}} =\:\frac{\pi}{\mathrm{4}}\:−\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\mathrm{2}{k}+\mathrm{1}} \\ $$$${calcilate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{U}_{{n}} \\ $$ Terms of…
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…