Question Number 16687 by tawa tawa last updated on 25/Jun/17 $$\mathrm{Three}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}\:\mathrm{form}\:\mathrm{the}\:\mathrm{three}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}, \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{G}.\mathrm{P}\:\mathrm{forms}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P}\:\mathrm{by} \\ $$$$\mathrm{adding}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{G}.\mathrm{P}\:\mathrm{to}\:\mathrm{itself}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{fifth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{G}.\mathrm{P}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 82225 by M±th+et£s last updated on 19/Feb/20 Commented by mathmax by abdo last updated on 19/Feb/20 $${let}\:{S}_{{n}} =\sum_{{p}={n}+\mathrm{1}} ^{{kn}} \:\frac{\mathrm{1}}{{p}}\:\Rightarrow{S}_{{n}} =\sum_{{p}=\mathrm{1}} ^{{kn}} \:\frac{\mathrm{1}}{{p}}−\sum_{{p}=\mathrm{1}}…
Question Number 147714 by puissant last updated on 22/Jul/21 $$\mathrm{Resoudre} \\ $$$$\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}^{\mathrm{2}} \right)\:>\:\mathrm{log}_{\mathrm{a}^{\mathrm{2}} } \left(\mathrm{3x}−\mathrm{2}\right) \\ $$$$\mathrm{avec}\:\:\mathrm{a}\in\mathbb{R}_{+} \backslash\left\{\mathrm{1}\right\} \\ $$$$\mathrm{NB}:\:\mathrm{a}\:\mathrm{et}\:\mathrm{a}^{\mathrm{2}} \:\mathrm{sont}\:\mathrm{les}\:\mathrm{bases}\:\mathrm{des}\:\mathrm{logarithmes} \\ $$$$\mathrm{des}\:\mathrm{nombres}\:\mathrm{de}\:\mathrm{l}'\mathrm{in}\acute {\mathrm{e}galite}..…
Question Number 16633 by tawa tawa last updated on 24/Jun/17 $$\sqrt{\mathrm{1}}\:.\:\sqrt{\mathrm{2}}\:.\:\sqrt{\mathrm{3}}.\:…\:\sqrt{\mathrm{n}}\:\:=\:\mathrm{S}_{\mathrm{n}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\:\mathrm{S}_{\mathrm{n}} \:? \\ $$ Commented by Arnab Maiti last updated on 02/Jul/17 $$\mathrm{S}_{\mathrm{n}}…
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Question Number 82019 by M±th+et£s last updated on 17/Feb/20 Answered by mind is power last updated on 18/Feb/20 $$\mathrm{2}{F}\mathrm{1}\left({k}+\mathrm{1},{k}+\mathrm{1};{k}+\mathrm{2};\mathrm{1}\right)=\left({k}+\mathrm{1}\right)\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{k}} \left(\mathrm{1}−{x}\right)^{−{k}−\mathrm{1}} {dx} \\ $$$${not}\:{defind}\:{sir}\:{tchek}\:{this}\:{Quation}…
Question Number 16450 by ajfour last updated on 22/Jun/17 $${Ten}\:{balls}\:{were}\:{manufactured}, \\ $$$$\:{nine}\:{of}\:{them}\:{have}\:{the}\:{same} \\ $$$${mass},\:{while}\:{just}\:{one}\:{of}\:{them} \\ $$$${has}\:{a}\:{slightly}\:{higher}\:{or}\:{slightly} \\ $$$${lower}\:{mass}.\:{Given}\:{is}\:{just}\:{a}\:{beam} \\ $$$${balance}\:{and}\:{no}\:{weights}.\:{comparing} \\ $$$${the}\:{masses}\:{of}\:{balls}\:{only},\:{with}\:{the} \\ $$$${help}\:{of}\:{the}\:{balance}\:,\:{and}\:{in}\:{just} \\…
Question Number 147493 by henderson last updated on 21/Jul/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{dears}}\:\boldsymbol{\mathrm{masters}}\:! \\ $$$$\boldsymbol{\mathrm{A}}\:=\:\left\{\boldsymbol{{au}}+\boldsymbol{{bv}},\:\left(\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{u}},\:\boldsymbol{{v}}\right)\:\in\:\mathbb{Z}^{\mathrm{4}} \right\}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{{a}}\:\neq\:\boldsymbol{{b}}. \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{ideal}}\:\boldsymbol{\mathrm{of}}\:\:\mathbb{Z}. \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{let}}\:\boldsymbol{\lambda}\mathbb{Z}\:=\:\left\{\boldsymbol{\lambda{n}}\:,\:\boldsymbol{{n}}\:\in\:\mathbb{Z}\right\}.\: \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{has}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{smaller}}\:\boldsymbol{\mathrm{element}}\:\boldsymbol{\lambda}\:\boldsymbol{\mathrm{strictly}}\: \\ $$$$\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{A}}\:=\:\boldsymbol{\lambda}\mathbb{Z}. \\ $$$$\mathrm{3}.\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\lambda}\:=\:\boldsymbol{\mathrm{gcd}}\left(\boldsymbol{{a}},\boldsymbol{{b}}\right). \\ $$…
Question Number 81911 by jagoll last updated on 16/Feb/20 Commented by jagoll last updated on 16/Feb/20 $${a}_{{n}+\mathrm{1}} \:=\:\frac{\mathrm{3}{a}_{{n}} +\mathrm{1}}{\mathrm{2}}\: \\ $$$${a}_{{n}+\mathrm{1}} \:+{A}\:=\:{A}+\frac{\mathrm{3}{a}_{{n}} +\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{3}{a}_{{n}} +\mathrm{2}{A}+\mathrm{1}}{\mathrm{2}} \\…
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