Question Number 61915 by aseerimad last updated on 11/Jun/19 $$\mathrm{1}+{iw}+\left({iw}\right)^{\mathrm{2}} +\left({iw}\right)^{\mathrm{3}} +………\left({iw}\right)^{\mathrm{989}} =? \\ $$$$ \\ $$$${ans}=\:\:\:\:\frac{\mathrm{2}}{\mathrm{1}−{iw}}\:\:\:\:\:\:{answer}\:{is}\:{correct}. \\ $$$${pls}\:{help}\:..\:{how}\:{to}\:{do}\:{this}? \\ $$$${TIA} \\ $$ Answered by…
Question Number 61843 by psyche last updated on 10/Jun/19 $$\boldsymbol{{let}}\:\boldsymbol{{V}}\:\:\:\boldsymbol{{be}}\:\boldsymbol{{a}}\:\boldsymbol{{vector}}\:\boldsymbol{{space}}\:\boldsymbol{{and}}\:\boldsymbol{{let}}\:\boldsymbol{{H}}\:\boldsymbol{{and}}\:\boldsymbol{{K}}\:\boldsymbol{{be}}\: \\ $$$$\boldsymbol{{subspace}}\:\boldsymbol{{of}}\:\boldsymbol{{V}}.\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:, \\ $$$${H}+{K}=\left\{\boldsymbol{{x}}:\boldsymbol{{x}}=\boldsymbol{{h}}+\boldsymbol{{k}},\:\boldsymbol{{where}}\:\boldsymbol{{h}}\in{H}\:\boldsymbol{{and}}\:\:\boldsymbol{{k}}\in{K}\right\}\:\boldsymbol{{is}}\:\:\boldsymbol{{a}}\:\boldsymbol{{subspace}}\:\boldsymbol{{of}}\:\boldsymbol{{V}}.\: \\ $$ Commented by arcana last updated on 10/Jun/19 $$\mathrm{if}\:\mathrm{V}\:\mathrm{is}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{space}\:\mathrm{over}\:\mathrm{a}\:\mathrm{field}\:\mathrm{K}. \\…
Question Number 61840 by psyche last updated on 10/Jun/19 $$\boldsymbol{{consider}}\:\boldsymbol{{the}}\:\boldsymbol{{triple}}\:\boldsymbol{{of}}\:\boldsymbol{{real}}\:\boldsymbol{{numbers}}\:\left(\boldsymbol{{x}},{y},{z}\right) \\ $$$${defined}\:{by}\:{the}\:{addittion}\:\left(\boldsymbol{{x}},{y},{z}\right)+\left({x}',{y}',{z}'\right)=\left({x}+{x}',{y}+{y}',{z}+{z}'\right) \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{scalar}}\:\boldsymbol{{multiplication}}\:\boldsymbol{{by}}\:\:\:\boldsymbol{\alpha}\left({x},{y},{z}\right)=\left(\mathrm{0},\mathrm{0},\mathrm{0}\right).\: \\ $$$$\boldsymbol{{S}}{how}\:{that}\:{all}\:{axioms}\:{for}\:{a}\:{vector}\:{space}\:{are}\:{satisfied}\:{except}\:{axiom}\:\mathrm{8}. \\ $$ Answered by arcana last updated on 10/Jun/19…
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Question Number 127295 by Dwaipayan Shikari last updated on 28/Dec/20 $$\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{{tanh}^{−\mathrm{1}} {x}}{\:\sqrt[{\mathrm{5}}]{{x}}}{dx}\:\:\:\:\:\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61755 by arcana last updated on 08/Jun/19 $$\mathrm{if}\:{f}\left({z}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{a}_{{k}} {z}^{{k}} ,{a}_{{k}} ,{z}\in\mathbb{C}.\mathrm{Prove} \\ $$$$ \\ $$$${a}_{{k}} =\frac{\mathrm{1}}{\mathrm{2}\pi{i}}\underset{\mid{z}\mid={r}\:} {\int}\frac{{f}\left({z}\right)}{{z}^{{k}+\mathrm{1}} }{dz} \\ $$$$ \\…
Question Number 127293 by Dwaipayan Shikari last updated on 28/Dec/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left({n}\right)}{{n}^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 61744 by Cheyboy last updated on 08/Jun/19 $$\mathrm{3}{xy}^{\mathrm{2}} +{x}^{\mathrm{3}} =\mathrm{9}\:−−−−−\left(\mathrm{1}\right) \\ $$$$\mathrm{3}{x}^{\mathrm{2}} {y}+{y}^{\mathrm{3}} =\mathrm{18}−−−−\left(\mathrm{2}\right) \\ $$$${Find}\:{x}\:{and}\:{y} \\ $$ Commented by Cheyboy last updated…
Question Number 192791 by Mastermind last updated on 27/May/23 $$\mathrm{If}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{2}^{\mathrm{n}} \Gamma\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{1}.\mathrm{3}.\mathrm{5}…\left(\mathrm{2n}−\mathrm{1}\right)\sqrt{\pi}. \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$ Answered by Mathspace last updated on…