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Author: Tinku Tara

if-a-gt-0-b-gt-0-a-b-show-that-a-2-2ab-a-b-2-ab-a-b-2-2-a-2-b-2-2-b-2-

Question Number 82667 by M±th+et£s last updated on 23/Feb/20 $${if}\:{a}>\mathrm{0}\:\:{b}>\mathrm{0}\:\:{a}\leqslant{b} \\ $$$$ \\ $$$${show}\:{that}\: \\ $$$${a}^{\mathrm{2}} \leqslant\left(\frac{\mathrm{2}{ab}}{{a}+{b}}\right)^{\mathrm{2}} \leqslant{ab}\leqslant\left(\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} \leqslant\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}}\leqslant{b}^{\mathrm{2}} \\ $$ Answered by…

n-1-8-n-2-n-

Question Number 148203 by liberty last updated on 26/Jul/21 $$\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{8}}{{n}^{\mathrm{2}} +{n}}\right)=? \\ $$ Answered by mathmax by abdo last updated on 26/Jul/21 $$\mathrm{S}=\mathrm{8}\sum_{\mathrm{n}=\mathrm{1}}…

Question-17129

Question Number 17129 by virus last updated on 01/Jul/17 Answered by ajfour last updated on 01/Jul/17 $$\mathrm{v}_{\mathrm{avg}} =\frac{\mid\bigtriangleup\boldsymbol{\mathrm{r}}\mid}{\bigtriangleup\mathrm{t}}=\frac{\mathrm{2rsin}\:\left(\theta/\mathrm{2}\right)}{\mathrm{r}\theta/\mathrm{v}} \\ $$$$\:\:\:\:\:\:\:=\:\mathrm{v}\left[\frac{\mathrm{sin}\:\left(\theta/\mathrm{2}\right)}{\left(\theta/\mathrm{2}\right)}\right]\:, \\ $$$$\mathrm{a}_{\mathrm{avg}} =\frac{\mid\bigtriangleup\boldsymbol{\mathrm{v}}\mid}{\bigtriangleup\mathrm{t}}=\frac{\mathrm{2vsin}\:\left(\theta/\mathrm{2}\right)}{\mathrm{r}\theta/\mathrm{v}} \\ $$$$\:\:\:\:\:\:\:=\:\frac{\mathrm{v}^{\mathrm{2}}…