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Category: Relation and Functions

let-S-x-n-1-1-n-1-x-2n-1-4n-2-1-1-find-the-radius-of-convergence-2-calculate-the-sum-S-x-

Question Number 34309 by prof Abdo imad last updated on 03/May/18 $${let}\:{S}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:\:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{4}{n}^{\mathrm{2}} \:−\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{radius}\:{of}\:{convergence} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{the}\:{sum}\:\:{S}\left({x}\right). \\ $$ Commented by…

let-x-0-1-and-x-n-1-ln-e-x-n-x-n-1-prove-that-x-n-0-2-prove-that-x-n-converges-and-ddyermine-its-sum-

Question Number 99839 by mathmax by abdo last updated on 23/Jun/20 $$\mathrm{let}\:\mathrm{x}_{\mathrm{0}} =\mathrm{1}\:\mathrm{and}\:\mathrm{x}_{\mathrm{n}+\mathrm{1}} =\mathrm{ln}\left(\mathrm{e}^{\mathrm{x}_{\mathrm{n}} } −\mathrm{x}_{\mathrm{n}} \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{prove}\:\mathrm{that}\:\mathrm{x}_{\mathrm{n}} \:\rightarrow\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\mathrm{prove}\:\mathrm{that}\:\Sigma\:\mathrm{x}_{\mathrm{n}} \:\mathrm{converges}\:\mathrm{and}\:\mathrm{ddyermine}\:\mathrm{its}\:\mathrm{sum} \\ $$…

let-A-2-1-1-2-1-calculate-A-n-2-determine-cosA-and-sinA-3-find-chA-and-shA-

Question Number 99828 by mathmax by abdo last updated on 23/Jun/20 $$\mathrm{let}\:\mathrm{A}\:=\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\mathrm{2}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{A}^{\mathrm{n}} \\ $$$$\left.\mathrm{2}\right)\mathrm{determine}\:\mathrm{cosA}\:\mathrm{and}\:\mathrm{sinA} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{chA}\:\mathrm{and}\:\mathrm{shA} \\ $$ Commented by bachamohamed last updated…

calculate-I-0-dx-1-x-2-1-x-n-and-J-0-x-n-1-x-2-1-x-n-dx-with-n-integr-gt-0-

Question Number 34263 by math khazana by abdo last updated on 03/May/18 $${calculate}\:{I}\:\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{{n}} \right)}\:\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{x}^{{n}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{{n}} \right)}{dx}\:{with}\:{n}\:{integr}\:>\mathrm{0} \\…

1-prove-that-x-0-1-1-1-x-lnx-x-1-2-find-2-sequences-u-n-and-v-n-u-n-k-1-n-1-ln-k-n-v-n-n-2-

Question Number 34258 by math khazana by abdo last updated on 03/May/18 $$\left.\mathrm{1}\left.\right)\:{prove}\:{that}\:\forall\:{x}\in\right]\mathrm{0},\mathrm{1}\left[\:\:\mathrm{1}−\frac{\mathrm{1}}{{x}}\leqslant{lnx}\leqslant\:{x}−\mathrm{1}\right. \\ $$$$\left.\mathrm{2}\right)\:{find}\:\mathrm{2}\:{sequences}\:{u}_{{n}} \:{and}\:{v}_{{n}} \:\:\:/ \\ $$$${u}_{{n}} \leqslant\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:{ln}\left(\frac{{k}}{{n}}\right)\leqslant{v}_{{n}} \:\:\:\:\forall{n}\geqslant\mathrm{2} \\ $$…