Question Number 4719 by prakash jain last updated on 29/Feb/16 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +…+{a}_{{n}} }{{n}}\leqslant\sqrt{\frac{{a}_{\mathrm{1}} ^{\mathrm{2}} +{a}_{\mathrm{2}} ^{\mathrm{2}} +…+{a}_{{n}} ^{\mathrm{2}} }{{n}}} \\ $$$$\mathrm{with}\:\mathrm{equality}\:\mathrm{holding}\:\mathrm{iff}\:{a}_{\mathrm{1}} ={a}_{\mathrm{2}}…
Question Number 4720 by prakash jain last updated on 29/Feb/16 $$\mathrm{Prove}\:\mathrm{or}\:\mathrm{counterexample}\:\mathrm{that}\:\mathrm{if}\:\mathrm{a}\:\mathrm{finite}\:\mathrm{number}\: \\ $$$$\mathrm{of}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{series}\:\mathrm{are}\:\mathrm{given}\:\mathrm{then}\:\mathrm{a}\:\mathrm{infinite}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{formulas}\:\mathrm{for}\:{n}^{{th}} \:\mathrm{term}\:\mathrm{exists}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{finite}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}. \\ $$$$\mathrm{For}\:\mathrm{example} \\ $$$$\mathrm{33},\mathrm{9},\mathrm{33},\mathrm{44},? \\ $$$$\mathrm{4}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{given}\:\mathrm{if}\:{a}_{{n}} ={f}\left({n}\right)\:\mathrm{then}\:\mathrm{there}\:\mathrm{are}…
Question Number 135786 by JulioCesar last updated on 16/Mar/21 Commented by Ar Brandon last updated on 16/Mar/21 $$\mathrm{You}\:\mathrm{mean}\: \\ $$$$\mathrm{H}=\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{9}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}} }}\:??? \\ $$…
Question Number 135771 by 7514418113 last updated on 15/Mar/21 $$ \\ $$ Commented by SWPlaysMC last updated on 15/Mar/21 $${No}\:{question}\:{available}.\:{Please}\:{enter}\:{a}\:{question}\:{for}\:{us}\:{to}\:{solve}.\:−{SWPlaysMC} \\ $$ Terms of Service…
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Question Number 70216 by mathmax by abdo last updated on 02/Oct/19 $${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right){calculate}\:{A}^{{n}} \:\:\:\:\: \\ $$$$\left.\mathrm{2}\right)\:{find}\:{e}^{{A}} \:{and}\:{e}^{−{A}} \\ $$ Terms of Service Privacy Policy…
Question Number 4670 by malwaan last updated on 20/Feb/16 $${prove}\:{that} \\ $$$$\mathrm{0}.\mathrm{101101110}\rightarrow\: \\ $$$${irrational}\:{number} \\ $$ Commented by prakash jain last updated on 21/Feb/16 $$\mathrm{Non}−\mathrm{recurring}\:\mathrm{non}−\mathrm{terminating}\:\mathrm{decimals}…
Question Number 4653 by FilupSmith last updated on 18/Feb/16 $$\mathrm{Silly}\:\mathrm{question} \\ $$$${which}\:{is}\:{correct}??? \\ $$$$ \\ $$$$\mathrm{ln}\left(\frac{{n}}{{ab}}\right)=\mathrm{ln}\left({n}\right)−\mathrm{ln}\left({ab}\right)=\mathrm{ln}\left({n}\right)−\mathrm{ln}\left({a}\right)+\mathrm{ln}\left({b}\right) \\ $$$${or} \\ $$$$\mathrm{ln}\left(\frac{{n}}{{ab}}\right)=\mathrm{ln}\left({n}\right)−\mathrm{ln}\left({ab}\right)=\mathrm{ln}\left({n}\right)−\mathrm{ln}\left({a}\right)−\mathrm{ln}\left({b}\right) \\ $$ Answered by 123456…
Question Number 4630 by sanusihammed last updated on 15/Feb/16 $${Solve}\:{for}\:{x}\:{in}\:{the}\:{equation} \\ $$$$\mathrm{4}^{{x}\:} =\:\mathrm{8}{x} \\ $$$$ \\ $$$${I}\:{know}\:{the}\:{answer}\:{is}\:\mathrm{2}.\:{I}\:{need}\:{the}\:{solution}.\:{Thanks} \\ $$$$ \\ $$ Commented by FilupSmith last…
Question Number 70162 by TawaTawa last updated on 01/Oct/19 Answered by mind is power last updated on 01/Oct/19 $$\Rightarrow\mathrm{1}=\left({a}+{b}\right)\left(\frac{{sin}^{\mathrm{4}} \left(\theta\right)}{{a}}+\frac{{cos}^{\mathrm{4}} \left(\theta\right)}{{b}}\right)…{S} \\ $$$$\Rightarrow\frac{{b}}{{a}}{Sin}^{\mathrm{4}} \left(\theta\right)+\frac{{a}}{{b}}{cos}^{\mathrm{4}} \left(\theta\right)+{cos}^{\mathrm{4}}…