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Question-195612

Question Number 195612 by Mastermind last updated on 05/Aug/23 Answered by a.lgnaoui last updated on 05/Aug/23 $$\mathrm{r}−\mathrm{73}=\pm\mathrm{16} \\ $$$$\begin{cases}{\mathrm{r}−\mathrm{73}=\mathrm{16}\:\:\:\:\:\:\:\:\Rightarrow\:\:\boldsymbol{\mathrm{r}}=\mathrm{89}}\\{\boldsymbol{\mathrm{r}}−\mathrm{73}=−\mathrm{16}\:\:\:\Rightarrow\:\:\boldsymbol{\mathrm{r}}=\mathrm{57}}\end{cases} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{r}}=\left\{\mathrm{57},\mathrm{89}\right\} \\ $$ Terms of…

Question-195412

Question Number 195412 by Calculusboy last updated on 02/Aug/23 Answered by AST last updated on 02/Aug/23 $${v}_{\mathrm{2}} \left({a}^{\mathrm{2}^{{n}} } −\mathrm{1}\right)={v}_{\mathrm{2}} \left({a}−\mathrm{1}\right)+{n}+{v}_{\mathrm{2}} \left({a}+\mathrm{1}\right)−\mathrm{1}\geqslant{n}+\mathrm{2} \\ $$$$\Rightarrow\mathrm{2}^{{n}+\mathrm{2}} \mid{a}^{\mathrm{2}^{{n}}…

Calculer-la-valeur-de-la-serie-suivante-S-3-2-5-8-7-32-9-128-

Question Number 195129 by a.lgnaoui last updated on 25/Jul/23 $$\mathrm{Calculer}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{de}\:\mathrm{la}\:\mathrm{serie}\:\mathrm{suivante}: \\ $$$$\boldsymbol{\mathrm{S}}=\frac{\mathrm{3}}{\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{8}}+\frac{\mathrm{7}}{\mathrm{32}}+\frac{\mathrm{9}}{\mathrm{128}}+….. \\ $$ Answered by MM42 last updated on 25/Jul/23 $$\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }{S}=\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{5}}{\mathrm{2}^{\mathrm{5}} }+\frac{\mathrm{7}}{\mathrm{2}^{\mathrm{7}}…

Question-194878

Question Number 194878 by oMwarimu last updated on 18/Jul/23 Answered by Rasheed.Sindhi last updated on 18/Jul/23 $${a}+{d}={ar}^{\mathrm{3}} \:\:\wedge\:\:{a}+\mathrm{9}{d}={ar}^{\mathrm{6}} \\ $$$${a}\left({r}^{\mathrm{3}} −\mathrm{1}\right)={d}\:\wedge\:{a}\left({r}^{\mathrm{6}} −\mathrm{1}\right)=\mathrm{9}{d} \\ $$$${a}=\frac{{d}}{{r}^{\mathrm{3}} −\mathrm{1}}\:\wedge\:{a}=\frac{\mathrm{9}{d}}{{r}^{\mathrm{6}}…