Question Number 187025 by Rupesh123 last updated on 12/Feb/23 Answered by a.lgnaoui last updated on 12/Feb/23 $${E} \\ $$ Commented by Rupesh123 last updated on…
Question Number 55869 by mr W last updated on 05/Mar/19 $${if}\:\boldsymbol{{a}}_{\boldsymbol{{n}}+\mathrm{2}} =\frac{\boldsymbol{{a}}_{\boldsymbol{{n}}+\mathrm{1}} ^{\mathrm{3}} }{\boldsymbol{{a}}_{\boldsymbol{{n}}} ^{\mathrm{2}} }\:{and}\:{a}_{\mathrm{1}} =\mathrm{2},\:{a}_{\mathrm{2}} =\mathrm{4} \\ $$$${find}\:\boldsymbol{{a}}_{\boldsymbol{{n}}} =? \\ $$ Commented by…
Question Number 186884 by Mingma last updated on 11/Feb/23 Commented by mr W last updated on 11/Feb/23 $${you}\:{are}\:{asking}\:{questions}\:{non}−{stop}, \\ $$$${but}\:{you}\:{seem}\:{never}\:{to}\:{give}\:{any}\:{feed} \\ $$$${back}:\:{no}\:{thanks}\:{to}\:{people}\:{who}\: \\ $$$${answered}\:{your}\:{questions},\:{no}\: \\…
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Question Number 55674 by gunawan last updated on 01/Mar/19 $$\mathrm{The}\:\mathrm{smallest}\:\mathrm{integer}\:\mathrm{numbers} \\ $$$$\mathrm{with}\:{n}\:\geqslant\:\mathrm{2018}\:\mathrm{so} \\ $$$$\left(\sqrt{\mathrm{3}}+\mathrm{3}{i}\right)^{{n}} \:\mathrm{form}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{is}.. \\ $$ Answered by mr W last updated on 02/Mar/19…
Question Number 55628 by Mikael_Marshall last updated on 28/Feb/19 $${In}\:{an}\:{A}.{P},\:{the}\:{sum}\:{of}\:{the}\:{first}\:\mathrm{50}\:{terms}\:{is}\:\mathrm{6275}.\:{Write}\:\:{this}\:{A}.{P}\:.\:{knowing}\:{that}\:{the}\:{ratio}\:{is}\:\mathrm{5}. \\ $$ Answered by kaivan.ahmadi last updated on 28/Feb/19 $${s}_{{n}} =\frac{{n}}{\mathrm{2}}\left[\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right] \\ $$$$\mathrm{6275}=\mathrm{25}\left[\mathrm{2}{a}+\mathrm{49}×\mathrm{5}\right]=\mathrm{25}\left[\mathrm{2}{a}+\mathrm{245}\right]= \\ $$$$\mathrm{50}{a}+\mathrm{6145}\Rightarrow\mathrm{50}{a}=\mathrm{6275}−\mathrm{6145}=\mathrm{150}\Rightarrow…
Question Number 121066 by Jamshidbek2311 last updated on 05/Nov/20 $$\left.\mathrm{1}\right)\int\frac{{x}}{{x}+\mathrm{1}}{dx}=? \\ $$$$\left.\mathrm{2}\right)\int\frac{{x}}{\:\sqrt{{x}−\mathrm{1}}}{dx}=? \\ $$$$\left.\mathrm{3}\right)\int{x}\sqrt{{x}−\mathrm{4}}{dx}=\overset{} {?} \\ $$$$ \\ $$ Commented by liberty last updated on…
Question Number 186597 by Mingma last updated on 06/Feb/23 Answered by Frix last updated on 07/Feb/23 $$\mathrm{123} \\ $$$$\mathrm{132} \\ $$$$\mathrm{213} \\ $$$$\mathrm{231} \\ $$$$\mathrm{312}…
Question Number 121014 by mathocean1 last updated on 04/Nov/20 $$\mathrm{show}\:\mathrm{by}\:\mathrm{recurrence}\:\mathrm{that} \\ $$$$\forall\:\mathrm{n}\geqslant\mathrm{1}\:, \\ $$$$\mathrm{a}^{\mathrm{n}} −\mathrm{b}^{\mathrm{n}} =\left(\mathrm{a}−\mathrm{b}\right)\left(\mathrm{a}^{\mathrm{n}−\mathrm{1}} +\mathrm{a}^{\mathrm{n}−\mathrm{2}} \ast\mathrm{b}+…+\mathrm{ab}^{\mathrm{n}−\mathrm{2}} +\mathrm{b}^{\mathrm{n}−\mathrm{1}} \right) \\ $$ Answered by mathmax…
Question Number 121012 by mathocean1 last updated on 04/Nov/20 $$\mathrm{x};\mathrm{y};\mathrm{z}\:\in\:\mathbb{N}^{\ast\:} \mathrm{with}\:\mathrm{x}>\mathrm{3}\:\mathrm{are}\: \\ $$$$\mathrm{numbers}. \\ $$$$\mathrm{we}\:\mathrm{suppose}\:\mathrm{that}\:\mathrm{y}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{121}\:\mathrm{in}\:\mathrm{base}\:\mathrm{x}\:\mathrm{and}\:\mathrm{z}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{110}\:\mathrm{in}\:\mathrm{base}\:\mathrm{x}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{show}\:\mathrm{that}\:\mathrm{we}\:\mathrm{can}\:\mathrm{write} \\ $$$$\left(\mathrm{without}\:\mathrm{knowing}\:\mathrm{x}\right)\:\mathrm{the}\: \\ $$$$\mathrm{product}\:\mathrm{xyz}\:\mathrm{in}\:\mathrm{base}\:\mathrm{x}.…