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}}…
Question Number 28620 by abdo imad last updated on 28/Jan/18 $${calculate}\:\:\sum_{{n}={p}} ^{+\infty} \:\:\:{C}_{{n}\:} ^{{p}} {x}^{{n}} . \\ $$ Commented by Tinkutara last updated on 28/Jan/18…
Question Number 28618 by abdo imad last updated on 27/Jan/18 $${let}\:{give}\:{u}_{{n}} =\:\sum_{{k}={n}} ^{+\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{\:\sqrt{{k}+\mathrm{1}}}\:\:{study}\:{the}\:{convergence}\:{of}\: \\ $$$$\Sigma\:{u}_{{n}} . \\ $$ Terms of Service Privacy Policy…
Question Number 28617 by abdo imad last updated on 27/Jan/18 $${let}\:{give}\:{a}\:{sequence}\:{of}\:{reals}\:\left({a}_{{n}} \right)_{{n}} \:\:/\:{a}_{{n}} >\mathrm{0}\:\:{and} \\ $$$${U}_{{n}} =\:\:\:\frac{{a}_{{n}} }{\left(\mathrm{1}+{a}_{\mathrm{1}} \right)\left(\mathrm{1}+{a}_{\mathrm{2}} \right)….\left(\mathrm{1}+{a}_{{n}} \right)} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\Sigma\:{u}_{{n}} \:{converges} \\…
Question Number 28612 by abdo imad last updated on 27/Jan/18 $${let}\:{give}\:\:{u}_{{n}\:} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{sin}\left({k}\alpha\right)}{{n}+{k}}\:{and}\:\:\alpha\in{R} \\ $$$${find}\:{lim}\:_{{n}\rightarrow+\infty} {u}_{{n}} \:\:. \\ $$ Terms of Service Privacy Policy…
Question Number 159668 by Ar Brandon last updated on 19/Nov/21 $$\mathrm{Study}\:\mathrm{the}\:\mathrm{nature}\:\mathrm{of} \\ $$$$\:\:\:\:\Sigma\frac{{n}^{{n}} }{\left(\mathrm{ln}{n}\right)^{{n}^{\mathrm{2}} } } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159670 by Ar Brandon last updated on 19/Nov/21 Answered by puissant last updated on 20/Nov/21 $$\left.\mathrm{1}\right) \\ $$$${U}_{{n}} =\frac{{n}}{{n}^{\mathrm{3}} +\mathrm{1}}\:\underset{+\infty} {\sim}\frac{{n}}{{n}^{\mathrm{3}} }\:=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:{ainsi},\:{si}\:{on}\:{compare}…
Question Number 159646 by cortano last updated on 19/Nov/21 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\left(\mathrm{cos}\:{x}\right)^{\mathrm{sin}\:{x}} }{{x}^{\mathrm{3}} }\:=? \\ $$ Answered by FongXD last updated on 19/Nov/21 $$\mathrm{L}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\left(\mathrm{cosx}\right)^{\mathrm{sinx}} }{\mathrm{x}^{\mathrm{3}}…
Question Number 159621 by mathlove last updated on 19/Nov/21 Commented by metamorfose last updated on 20/Nov/21 $${what}\:{x}??????\: \\ $$ Terms of Service Privacy Policy Contact:…