Question Number 7005 by Tawakalitu. last updated on 05/Aug/16 $${Is}\:\:{u}_{{n}} \:{real}\:{sequence}\:{defende}\:\:{by}\:\: \\ $$$${u}_{\mathrm{0}} \:=\:\mathrm{3}{e}^{{t}} \:{u}_{{n}+\mathrm{1}} \:=\:\mathrm{2}\left({u}_{{n}} \right)^{\mathrm{2}} \:−\:\mathrm{1} \\ $$$${Determine}\:{the}\:{general}\:{term}\:{u}_{{n}} \:{of}\:{this}\:{series}\: \\ $$$$\left({justify}\:{your}\:{answer}\:{and}\:{method}\:{used}\right) \\ $$$$…
Question Number 138003 by benjo_mathlover last updated on 09/Apr/21 Answered by EDWIN88 last updated on 09/Apr/21 $${begin}\:{from}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} }{{n}!}\:=\:{e}^{{x}} −\mathrm{1}\:.\:{Taking}\:{derivative} \\ $$$$\Rightarrow\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{nx}^{{n}−\mathrm{1}}…
Question Number 137635 by Dwaipayan Shikari last updated on 04/Apr/21 Commented by Dwaipayan Shikari last updated on 04/Apr/21 $${A}\:{friend}\:{of}\:{mine}\:{sent}\:{me}\:{this}.\:{I}\:{am}\:{posting}\:{this}\:{behalf}\:{of} \\ $$$${him} \\ $$ Terms of…
Question Number 137585 by bramlexs22 last updated on 04/Apr/21 $${Find}\:{the}\:{cube}\:{of}\:{the}\:{number}\: \\ $$$${N}=\:\sqrt{\mathrm{7}\sqrt{\mathrm{3}\sqrt{\mathrm{7}\sqrt{\mathrm{3}\sqrt{\mathrm{7}\sqrt{\mathrm{3}\sqrt{\mathrm{7}\sqrt{\mathrm{3}…}}}}}}}} \\ $$ Answered by bemath last updated on 04/Apr/21 $${N}=\mathrm{7}^{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{32}}+\frac{\mathrm{1}}{\mathrm{128}}+…} .\:\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{16}}+\frac{\mathrm{1}}{\mathrm{64}}+…} \\ $$$${N}=\mathrm{7}^{\frac{\mathrm{1}/\mathrm{2}}{\mathrm{1}−\mathrm{1}/\mathrm{4}}}…
Question Number 137579 by liberty last updated on 04/Apr/21 $$\left(−\mathrm{1}\right)×\frac{\mathrm{1}}{\pi.{i}}\:=?\: \\ $$ Answered by Engr_Jidda last updated on 04/Apr/21 $$\left(−\mathrm{1}\right)×\frac{\mathrm{1}}{\pi{i}}=\:{i}^{\mathrm{2}} \frac{\mathrm{1}}{\pi{i}}=\frac{{i}}{\pi} \\ $$ Terms of…
Question Number 137383 by bramlexs22 last updated on 02/Apr/21 $${What}\:{is}\:{the}\:{remainder}\:\mathrm{13}^{\mathrm{163}} \:{when} \\ $$$${divided}\:{by}\:\mathrm{99}\: \\ $$ Answered by EDWIN88 last updated on 02/Apr/21 $$\mathrm{By}\:\mathrm{Euler}\:\mathrm{Theorem}\: \\ $$$$\varphi\left(\mathrm{99}\right)\:=\:\mathrm{3}\left(\mathrm{3}−\mathrm{1}\right)\left(\mathrm{11}−\mathrm{1}\right)=\:\mathrm{60}\:…
Question Number 137364 by liberty last updated on 02/Apr/21 $${Find}\:{the}\:{remainder}\:\mathrm{7}^{\mathrm{30}} \:{divide} \\ $$$${by}\:\mathrm{10}\: \\ $$ Answered by MJS_new last updated on 02/Apr/21 $$\mathrm{7}^{\mathrm{0}} =\mathrm{1} \\…
Question Number 6280 by prakash jain last updated on 21/Jun/16 $$\mathrm{52}\::\:\mathrm{9}\:::\:\mathrm{48}\::\:\mathrm{31}\:::\:\mathrm{27}\::\:\mathrm{13}\:::\:\mathrm{65}\::\:? \\ $$ Commented by prakash jain last updated on 21/Jun/16 $$\mathrm{The}\:\mathrm{question}\:\mathrm{from}\:\mathrm{a}\:\mathrm{mental}\:\mathrm{ability}\:\mathrm{test}. \\ $$ Answered…
Question Number 71806 by ahmadshahhimat775@gmail.com last updated on 20/Oct/19 Answered by MJS last updated on 20/Oct/19 $$\left(−\mathrm{2}\right)^{\sqrt{\mathrm{2}}} =\left(\mathrm{2e}^{\mathrm{i}\pi} \right)^{\sqrt{\mathrm{2}}} =\mathrm{2}^{\sqrt{\mathrm{2}}} \mathrm{e}^{\mathrm{i}\pi\sqrt{\mathrm{2}}} = \\ $$$$=\mathrm{2}^{\sqrt{\mathrm{2}}} \mathrm{cos}\:\pi\sqrt{\mathrm{2}}\:+\mathrm{2}^{\sqrt{\mathrm{2}}}…
Question Number 6055 by 1771727373 last updated on 11/Jun/16 $${ln}\left({x}\right)+{x}={a} \\ $$$${x}=? \\ $$ Answered by Yozzii last updated on 11/Jun/16 $${lnx}={a}−{x}\Rightarrow{x}={e}^{{a}−{x}} \Rightarrow{xe}^{{x}} ={e}^{{a}} \\…