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Question Number 9824 by j.masanja06@gmail.com last updated on 06/Jan/17 Answered by sandy_suhendra last updated on 06/Jan/17 $$\left(\mathrm{i}\right) \\ $$$$\mathrm{AP}\:: \\ $$$$\mathrm{P}=\mathrm{a}−\mathrm{b} \\ $$$$\mathrm{2Q}=\mathrm{a}\:\Rightarrow\:\mathrm{Q}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{a} \\ $$$$\mathrm{R}=\mathrm{a}+\mathrm{b}…
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Question Number 140890 by mathsuji last updated on 13/May/21 $$\mathrm{1}+\mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}^{\mathrm{3}} +…+\left({n}+\mathrm{1}\right){x}^{\boldsymbol{{n}}} =? \\ $$ Answered by ajfour last updated on 14/May/21 $${x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +…+{x}^{{n}+\mathrm{1}}…
Question Number 140863 by mathdanisur last updated on 13/May/21 $$\mathrm{1}+\sqrt{\mathrm{3}^{\boldsymbol{{a}}} }\:=\:\mathrm{2}\sqrt{\mathrm{2}^{\boldsymbol{{a}}} } \\ $$ Commented by mr W last updated on 13/May/21 $${a}=\mathrm{0}\:{or}\:\mathrm{2} \\ $$…
Question Number 9784 by FilupSmith last updated on 04/Jan/17 $$\mathrm{For}\:\left({x}+{y}\right)^{{n}} :{n}\in\mathbb{Z} \\ $$$$\left({x}+{y}\right)^{{n}} =\underset{{u}=\mathrm{0}} {\overset{{n}} {\sum}}\begin{pmatrix}{{n}}\\{{u}}\end{pmatrix}\:{x}^{{n}−{u}} {y}^{{n}} \\ $$$$\: \\ $$$$\mathrm{Is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{generalization}\:\mathrm{for}\:\mathrm{when} \\ $$$${n}\:\mathrm{is}\:\mathrm{non}\:\mathrm{integer}? \\ $$$$\:…
Question Number 9778 by j.masanja06@gmail.com last updated on 02/Jan/17 $${find}\:{the}\:{relation}\:{between}\:{a},{b},\:{and}\:{c} \\ $$$${if}\:{the}\:{root}\:{of}\:{equatio}\:\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} \:+{cx}=\mathrm{0} \\ $$$${are}\:{in} \\ $$$$\left({i}\right){GP} \\ $$$$\left({ii}\right){Ap} \\ $$$$ \\ $$ Terms…
Question Number 75306 by 21042004 last updated on 09/Dec/19 $${Use}\:{Venn}\:{diagram}\:{to} \\ $$$${represent}\:{the}\:{set}\:{of}\:{natural} \\ $$$${numbers},\:{integers},\:{rational} \\ $$$${numbers},\:{irrational} \\ $$$${numbers},\:{real}\:{numbers}, \\ $$$${complex}\:{numbers} \\ $$ Commented by mr…
Question Number 75299 by 21042004 last updated on 09/Dec/19 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{this}? \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[\:\frac{\mathrm{1}}{\mathrm{10}^{{n}} }\:\right] \\ $$$$\left.\mathrm{a}\right)\:\mathrm{0}.\mathrm{00}…\mathrm{001} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{0} \\ $$$$\left.\mathrm{c}\right)\:\mathrm{uknown} \\ $$ Commented by 21042004…
Question Number 140834 by greg_ed last updated on 13/May/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{sirs}}\:! \\ $$$$\boldsymbol{\mathrm{please}},\:\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{thing}}\:\boldsymbol{\mathrm{below}}\:\left(\boldsymbol{{a}}\:\in\:\mathbb{R}\right)\: \\ $$$$\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}_{\mathrm{1}} −\boldsymbol{{x}}_{\mathrm{2}} \:=\:\boldsymbol{{a}}}\\{\boldsymbol{{x}}_{\mathrm{2}} −\boldsymbol{{x}}_{\mathrm{3}} \:=\:\mathrm{2}\boldsymbol{{a}}}\\{……………..}\\{……………..}\\{…………….}\\{\boldsymbol{{x}}_{\boldsymbol{{n}}−\mathrm{1}} −\:\boldsymbol{{x}}_{\boldsymbol{{n}}} \:=\:\left(\boldsymbol{{n}}−\mathrm{1}\right)\boldsymbol{{a}}}\\{\boldsymbol{{x}}_{\mathrm{1}} +\:\boldsymbol{{x}}_{\mathrm{2}} +\:…\:+\:\boldsymbol{{x}}_{\boldsymbol{{n}}−\mathrm{1}} +\:\boldsymbol{{x}}_{\boldsymbol{{n}}} \:=\:\boldsymbol{{na}}}\end{cases} \\…