Category: Relation and Functions

Question Number 31510 by abdo imad last updated on 09/Mar/18 $$\left.{find}\:{lim}_{{n}\rightarrow\infty} \:\:\:^{{n}} \sqrt{\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}}{{n}^{\mathrm{2}} }\right.}\right) \\ $$ Commented by abdo imad last updated on…

Question Number 31500 by abdo imad last updated on 09/Mar/18 $${let}\:{L}_{{n}} \left({x}\right)=\:{e}^{{x}} \:\left({e}^{−{x}} \:{x}^{{n}} \right)^{\left({n}\right)} \: \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{L}_{{n}} \:{is}\:{a}\:{polynomial} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{degL}_{{n}\:} {and}\:{the}\:{leading}\:{coefficient}\:. \\ $$ Commented…

Question Number 31422 by abdo imad last updated on 08/Mar/18 $${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{arctan}\left(\frac{\mathrm{2}}{\mathrm{16}{n}^{\mathrm{2}} \:+\mathrm{8}{n}−\mathrm{2}}\right). \\ $$ Commented by rahul 19 last updated on 08/Mar/18 $${can}\:{u}\:{plz}\:{provide}\:{sol}.\:{for}\:{this}\:{one}\:.…

Question Number 31417 by abdo imad last updated on 08/Mar/18 $${let}\:{give}\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\:−{ln}\left({n}\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{u}_{{n}} \:{is}\:{convergent}\: \\ $$$$\left.\mathrm{2}\right)\:{if}\:\:\:\gamma={lim}_{{n}\rightarrow\infty} {u}_{{n}} \:\:{prove}\:{the}\:\mathrm{0}<\gamma<\mathrm{1}\:. \\ $$ Terms of…

Question Number 96836 by mathmax by abdo last updated on 05/Jun/20 $$\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{wich}\:\mathrm{verify}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:+\mathrm{a}_{\mathrm{n}} =\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:\forall\mathrm{n} \\ $$$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \\ $$ Answered by Smail…