Question Number 28684 by abdo imad last updated on 28/Jan/18 $${find}\:\:{sum}\:{of}\:{S}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28681 by abdo imad last updated on 28/Jan/18 $${give}\:{a}\:{equivalent}\:{of}\:\:{w}_{{n}} =\:\:\:\sum_{{k}={n}+\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{k}!}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28682 by abdo imad last updated on 28/Jan/18 $${nature}\:{of}\:{the}\:{serie}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{tan}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{3}} }\right)\:. \\ $$ Commented by abdo imad last updated on 30/Jan/18 $${let}\:{put}\:{u}_{{n}}…
Question Number 159754 by cortano last updated on 20/Nov/21 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:{x}}\:+\:\sqrt{\mathrm{sin}\:{x}}\:−\mathrm{2}\sqrt{{x}}}{\:\sqrt{\mathrm{sin}\:{x}}\:−\:\sqrt{\mathrm{tan}\:{x}}\:}\:=\:? \\ $$ Answered by bobhans last updated on 21/Nov/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}\:+\sqrt{\mathrm{sin}\:\mathrm{x}}−\mathrm{2}\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{sin}\:\mathrm{x}}−\sqrt{\mathrm{tan}\:\mathrm{x}}}\: \\…
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Question Number 159727 by blackmamba last updated on 20/Nov/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt[{{x}^{\mathrm{3}} }]{\mathrm{1}+\mathrm{tan}\:\left(\mathrm{1}−\left(\frac{{x}}{\mathrm{sin}\:{x}}\right)\right)}\:?\: \\ $$ Answered by FongXD last updated on 20/Nov/21 $$\mathrm{L}=\underset{\mathrm{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\left[\mathrm{1}+\mathrm{tan}\left(\mathrm{1}−\frac{\mathrm{x}}{\mathrm{sinx}}\right)\right]^{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }}…
Question Number 159720 by tounghoungko last updated on 20/Nov/21 $$\:\:\:\:\:\:\:\:{L}\:=\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\mathrm{3}−\mathrm{4sin}\:^{\mathrm{2}} {x}}{\mathrm{sin}\:\mathrm{2}{x}−\mathrm{sin}\:{x}}\:? \\ $$$$\:\:\:\:\:\:{Q}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:\left(\frac{\mathrm{2}}{\mathrm{cos}\:^{\mathrm{2}} {x}}\:+\mathrm{cos}\:{x}−\mathrm{3}\right)\right]\:?\: \\ $$ Commented by cortano last updated on…
Question Number 28621 by abdo imad last updated on 28/Jan/18 $${let}\:{give}\:{u}_{{n}} =\frac{\left[\sqrt{\left.{n}+\mathrm{1}\right]}\:−\left[\sqrt{\left.{n}\right]}\right.\right.}{{n}}\:\:\:{find}\:\:\Sigma\:{u}_{{n}} \:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28622 by abdo imad last updated on 28/Jan/18 $${find}\:\:\sum_{{k}=\mathrm{0}} ^{+\infty} \:{arctan}\left(\:\frac{\mathrm{1}}{{k}^{\mathrm{2}} +{k}+\mathrm{1}}\right)\:. \\ $$ Commented by abdo imad last updated on 30/Jan/18 $${let}\:{put}\:{S}_{{n}}…
Question Number 28619 by abdo imad last updated on 27/Jan/18 $${calculate}\:\:\sum_{{k}=\mathrm{2}} ^{+\infty} \:{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\right)\:. \\ $$ Commented by abdo imad last updated on 31/Jan/18 $${let}\:{put}\:{S}_{{n}}…