Question Number 33347 by caravan msup abdo. last updated on 14/Apr/18 $${let}\:{f}_{{n}} \left({x}\right)=\:{nx}^{\mathrm{2}} \:{e}^{−{x}\sqrt{{n}}} \:\:\:,\:{x}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right){study}\:{the}\:{simple}\:{convergence}\:{of} \\ $$$$\Sigma\:{f}_{{n}} \left({x}\left\{\right.\right. \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{uniform}\:{convergence}\:{of} \\ $$$$\Sigma\:{f}_{{n}} \left({x}\right).…
Question Number 33337 by prof Abdo imad last updated on 14/Apr/18 $${let}\:\alpha>\mathrm{0}\:{prove}\:{that} \\ $$$$\sum_{{k}=\mathrm{1}} ^{{n}} \:\left(\mathrm{1}−\alpha\frac{{k}}{{n}}\right)_{{n}\rightarrow\infty} ^{{n}} \rightarrow\:\frac{{e}^{−\alpha} }{\mathrm{1}−{e}^{−\alpha} } \\ $$ Terms of Service…
Question Number 33335 by prof Abdo imad last updated on 14/Apr/18 $$\left.\mathrm{1}\right)\:{give}\:?{D}_{{n}−\mathrm{1}} \left({o}\right)\:\:{for}\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{{x}+\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{drcompose}\:{inside}\:{R}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)\:=\:\frac{\mathrm{1}}{{x}^{{n}} \left({x}+\mathrm{2}\right)} \\ $$ Commented by prof Abdo imad…
Question Number 33336 by prof Abdo imad last updated on 14/Apr/18 $${study}\:{the}\:{convergence}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} {ln}\left(\mathrm{1}+\frac{{x}}{{n}^{\mathrm{2}} }\right) \\ $$ Commented by prof Abdo imad last updated on…
Question Number 33316 by rahul 19 last updated on 14/Apr/18 $${If}\:\:\frac{{f}\left(\mathrm{2}{x}+\mathrm{2}{y}\right)}{{f}\left(\mathrm{2}{x}−\mathrm{2}{y}\right)}\:=\:\frac{\mathrm{sin}\:\left({x}+{y}\right)}{\mathrm{sin}\:\left({x}−{y}\right)}\:. \\ $$$${Then}\:{find}\:{f}\left({x}\right)\:? \\ $$ Answered by MJS last updated on 14/Apr/18 $$\mathrm{2}{x}\pm\mathrm{2}{y}=\mathrm{2}\left({x}\pm{y}\right)=\mathrm{2}{p} \\ $$$${f}\left(\mathrm{2}{p}\right)=\mathrm{sin}\:{p}\:=\:\mathrm{sin}\:\left({x}\pm{y}\right)…
Question Number 33308 by abdo imad last updated on 14/Apr/18 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{ln}\left({cos}\left(\frac{\alpha}{\mathrm{2}^{{n}} }\right)\right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33306 by abdo imad last updated on 14/Apr/18 $${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:{ln}\left(\:\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33304 by abdo imad last updated on 14/Apr/18 $${find}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:{ln}\left(\:\mathrm{1}+\frac{\mathrm{1}}{{n}}\right) \\ $$ Commented by abdo imad last updated on 19/Apr/18 $${let}\:{put}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}}…
Question Number 33305 by abdo imad last updated on 14/Apr/18 $${find}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\left(\mathrm{1}\:−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right) \\ $$ Commented by prof Abdo imad last updated on 15/Apr/18…
Question Number 33301 by abdo imad last updated on 14/Apr/18 $${calculate}\:\:\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\pi{nx}\right)}{\mathrm{2}^{{n}} }\:\:{and}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left(\pi{nx}\right)}{\mathrm{2}^{{n}} } \\ $$ Terms of Service Privacy Policy Contact:…