Question Number 63215 by mathmax by abdo last updated on 30/Jun/19 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \left\{{n}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} −{en}\right\} \\ $$ Commented by mathmax by abdo last updated on 01/Jul/19…
Question Number 63165 by mathmax by abdo last updated on 29/Jun/19 $${let}\:{W}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:\:\:{determine}\:{W}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$${H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$ Terms of…
Question Number 63164 by mathmax by abdo last updated on 29/Jun/19 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\:\:\:\:\:{and}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$$${calculate}\:{S}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}}…
Question Number 63101 by mathmax by abdo last updated on 29/Jun/19 $${calculate}\:\:{S}\:=\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}}\:+….. \\ $$ Commented by mathmax by abdo last updated on 29/Jun/19 $${let}\:{try}\:{another}\:{way}\:{we}\:{have}\:\frac{{d}}{{dx}}{ln}\left(\mathrm{1}+{x}\right)\:=\frac{\mathrm{1}}{\mathrm{1}+{x}}\:=\sum_{{n}=\mathrm{0}} ^{\infty}…
Question Number 128498 by mathmax by abdo last updated on 07/Jan/21 $$\mathrm{simplify}\:\mathrm{A}_{\mathrm{n}} =\frac{\mathrm{1}}{\left(\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{i}\right)^{\mathrm{n}} }+\frac{\mathrm{1}}{\left(\mathrm{1}−\sqrt{\mathrm{3}}\mathrm{i}\right)^{\mathrm{n}} } \\ $$ Answered by TheSupreme last updated on 08/Jan/21 $$\mathrm{1}+{i}\sqrt{\mathrm{3}}=\mathrm{2}{e}^{{i}\frac{\pi}{\mathrm{3}}}…
Question Number 62962 by fyyac c last updated on 27/Jun/19 $${P}\left({x}\right)=\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{2}{n}+\mathrm{1}}\: \\ $$$${P}_{\mathrm{1000}} \left({x}\right)=?\:{what}\:{is}\:{this}\:{sum}\:{in}\:{terms}\:{of}\:{x}? \\ $$ Terms of Service Privacy…
Question Number 128497 by mathmax by abdo last updated on 07/Jan/21 $$\mathrm{calvulate}\:\mathrm{A}\:=\frac{\mathrm{1}}{\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)^{\mathrm{6}} }+\frac{\mathrm{1}}{\left(\sqrt{\mathrm{3}}+\mathrm{1}\right)^{\mathrm{6}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128496 by mathmax by abdo last updated on 07/Jan/21 $$\mathrm{calculate}\:\:\:\mathrm{A}\:=\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{6}}\right)^{\mathrm{4}} }+\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{6}}\right)^{\mathrm{4}} } \\ $$ Commented by liberty last updated on 08/Jan/21 $$\frac{\left(\mathrm{2}−\sqrt{\mathrm{6}}\right)^{\mathrm{4}} +\left(\mathrm{2}+\sqrt{\mathrm{6}}\right)^{\mathrm{4}}…
Question Number 62924 by mathmax by abdo last updated on 26/Jun/19 $${find}\:{min}_{\left({a},{b}\right)\in{R}^{\mathrm{2}} } \:\:\:\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \left({ax}+{b}\right)^{\mathrm{2}} {dx} \\ $$ Commented by kaivan.ahmadi last updated on…
Question Number 128425 by bramlexs22 last updated on 07/Jan/21 $$\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}\:+\:\mathrm{tan}\:\mathrm{x}\:\mathrm{and}\:\mathrm{f}\:\mathrm{is}\:\mathrm{inverse} \\ $$$$\mathrm{of}\:\mathrm{g}\:,\:\mathrm{then}\:\mathrm{g}'\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{1}}{\mathrm{1}+\left(\mathrm{g}\left(\mathrm{x}\right)−\mathrm{x}\right)^{\mathrm{2}} }\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{1}}{\mathrm{1}−\left(\mathrm{g}\left(\mathrm{x}\right)−\mathrm{x}\right)^{\mathrm{2}} } \\ $$$$\left(\mathrm{c}\right)\:\frac{\mathrm{1}}{\mathrm{2}+\left(\mathrm{g}\left(\mathrm{x}\right)−\mathrm{x}\right)^{\mathrm{2}} }\:\:\:\left(\mathrm{d}\right)\:\frac{\mathrm{1}}{\mathrm{2}−\left(\mathrm{g}\left(\mathrm{x}\right)−\mathrm{x}\right)^{\mathrm{2}} } \\ $$ Answered by liberty…