Question Number 83026 by naka3546 last updated on 27/Feb/20 $${Prove}\:\:{that} \\ $$$$\:\:\:\:\:\mathrm{123456}..\mathrm{201820192020}\:\:{divided}\:\:{by}\:\:\mathrm{13}\:\:,\:\:{the} \\ $$$${remainder}\:\:{is}\:\:\mathrm{5}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 148519 by learner001 last updated on 28/Jul/21 $$ \\ $$$$\mathrm{a}_{\mathrm{n}} =\frac{\mathrm{n}}{\mathrm{n}+\mathrm{1}} \\ $$$$\mathrm{let}\:\epsilon>\mathrm{0}\:\mathrm{be}\:\mathrm{given},\:\mid\mathrm{a}_{\mathrm{m}} −\mathrm{a}_{\mathrm{n}} \mid=\mid\frac{\mathrm{m}}{\mathrm{m}+\mathrm{1}}−\frac{\mathrm{n}}{\mathrm{n}+\mathrm{1}}\mid=\mid\frac{\mathrm{m}−\mathrm{n}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}\mid=\frac{\mathrm{m}−\mathrm{n}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}\:\mathrm{provided} \\ $$$$\mathrm{m}>\mathrm{n},\:\frac{\mathrm{m}−\mathrm{n}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}<\frac{\mathrm{m}+\mathrm{1}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}=\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}<\epsilon.\:\mathrm{if}\:\mathrm{N}>\frac{\mathrm{1}−\epsilon}{\epsilon}\:\mathrm{then}\:\mid\mathrm{a}_{\mathrm{m}} −\mathrm{a}_{\mathrm{n}} \mid<\epsilon\:\forall\:\mathrm{n},\mathrm{m}\geqslant\mathrm{N} \\ $$ Commented by…
Question Number 17438 by Ruth1 last updated on 05/Jul/17 $$\mathrm{find}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{value}\:\mathrm{and}\:\mathrm{root}\:\mathrm{mean}\:\mathrm{square}\:\mathrm{of}\: \\ $$$$\mathrm{i}=\mathrm{25sin100}\Pi\mathrm{t}\:\:\:\:\:\mathrm{ranging}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{10} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 82953 by TawaTawa1 last updated on 26/Feb/20 $$\mathrm{verify}\:\mathrm{that}:\:\:\:\:\:\:\mathrm{cosh}.\mathrm{cosh}^{−\mathrm{1}} \left(\mathrm{y}\right)\:\:\:=\:\:\:\mathrm{y},\:\:\:\:\:\mathrm{if}\:\:\:\:\:\mathrm{y}\:\:\in\:\:\left(\mathrm{1},\:\:\:+\:\infty\right) \\ $$ Commented by mathmax by abdo last updated on 26/Feb/20 $${we}\:{have}\:{ch}^{−\mathrm{1}} \left({y}\right)={ln}\left({y}+\sqrt{{y}^{\mathrm{2}} −\mathrm{1}}\right)\:\Rightarrow…
Question Number 148437 by aliibrahim1 last updated on 28/Jul/21 Answered by mathmax by abdo last updated on 28/Jul/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}+\mathrm{x}}+\sqrt{\mathrm{1}−\mathrm{x}}}\:\Rightarrow\mathrm{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{\mathrm{1}+\mathrm{x}}−\sqrt{\mathrm{1}−\mathrm{x}}}{\mathrm{1}+\mathrm{x}−\mathrm{1}+\mathrm{x}}\mathrm{dx} \\ $$$$=\int_{\mathrm{0}}…
Question Number 148443 by peter frank last updated on 28/Jul/21 $${Can}\:{i}\:{use}\:{this}\:{app}\:\:{on}\:{PC} \\ $$$${to}\:{tinkutara} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 148428 by 0731619 last updated on 27/Jul/21 Answered by Mathspace last updated on 27/Jul/21 $$\frac{\left({a}+{b}\right)^{\mathrm{2}} }{{ab}}−\mathrm{3}\:=\frac{\left({a}+{b}\right)^{\mathrm{2}} −\mathrm{3}{ab}}{{ab}} \\ $$$$=\frac{{a}^{\mathrm{2}} +\mathrm{2}{ab}+{b}^{\mathrm{2}} −\mathrm{3}{ab}}{{ab}} \\ $$$$=\frac{{a}^{\mathrm{2}}…
Question Number 148427 by Rustambek last updated on 27/Jul/21 Answered by Ar Brandon last updated on 27/Jul/21 $$\mathrm{S}=\mathrm{2}+\underset{\mathrm{k}=\mathrm{2}} {\overset{\mathrm{2020}} {\sum}}\frac{\left(\mathrm{k}+\mathrm{1}\right)\mathrm{k}}{\frac{\mathrm{1}}{\mathrm{k}!}+\frac{\mathrm{1}}{\left(\mathrm{k}−\mathrm{1}\right)!}} \\ $$$$\:\:\:=\mathrm{2}+\underset{\mathrm{k}=\mathrm{2}} {\overset{\mathrm{2020}} {\sum}}\frac{\mathrm{k}\left(\mathrm{k}+\mathrm{1}\right)!}{\mathrm{1}+\mathrm{k}}=\mathrm{2}+\underset{\mathrm{k}=\mathrm{2}} {\overset{\mathrm{2020}}…
Question Number 17336 by chux last updated on 04/Jul/17 $$\mathrm{The}\:\mathrm{last}\:\mathrm{time}\:\mathrm{Nkechi}\:\mathrm{was}\:\mathrm{at}\:\mathrm{school} \\ $$$$\mathrm{was}\:\mathrm{on}\:\mathrm{Saturday}.\mathrm{She}\:\mathrm{was}\:\mathrm{first} \\ $$$$\mathrm{absent}\:\mathrm{for}\:\mathrm{4days}\:\mathrm{before}\:\mathrm{that}. \\ $$$$\mathrm{Today}\:\mathrm{is}\:\mathrm{Tuesday},\mathrm{27th}\:\mathrm{of}\: \\ $$$$\mathrm{September}.\mathrm{When}\:\mathrm{was}\:\mathrm{Nkechi} \\ $$$$\mathrm{first}\:\mathrm{absent}?\mathrm{Give}\:\mathrm{the}\:\mathrm{day}\:\mathrm{and} \\ $$$$\mathrm{date}.\mathrm{Select}\:\mathrm{one}: \\ $$$$\mathrm{1}.\mathrm{Monday}\:\mathrm{september}\:\mathrm{12} \\…
Question Number 148382 by VivianWilliam last updated on 27/Jul/21 $$\mathrm{0}.\mathrm{8\%}×\mathrm{544} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com