Category: Algebra

Question Number 140890 by mathsuji last updated on 13/May/21 $$1+2x+3x^2+4x^3+\dots +(n+1)x^{\mathit{n}}=?$$ Answered by ajfour last updated on 14/May/21 $${x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +…+{x}^{{n}+\mathrm{1}}…

Question Number 9784 by FilupSmith last updated on 04/Jan/17 $$\mathrm{For}{(x+y)}^n:n\in \mathbb{Z}$$$${(x+y)}^n=\underset{u=0}{\sum ^n}\left(\begin{array}{c}n\\ u\end{array}\right)x^{n-u}{y}^n$$$$$$$$\mathrm{Is}\mathrm{there}\mathrm{a}\mathrm{generalization}\mathrm{for}\mathrm{when}$$$$n\mathrm{is}\mathrm{non}\mathrm{integer}?$$$$\:…

Question Number 75306 by 21042004 last updated on 09/Dec/19 $$UseVenndiagramto$$$$representthesetofnatural$$$$numbers,integers,rational$$$$numbers,irrational$$$$numbers,realnumbers,$$$$complexnumbers$$ Commented by mr…

Question Number 140834 by greg_ed last updated on 13/May/21 $$\mathbf{hi},\mathbf{sirs}!$$$$\mathbf{please},\mathbf{how}\mathbf{to}\mathbf{solve}\mathbf{this}\mathbf{thing}\mathbf{below}(\mathit{a}\in \mathbb{R})$$$$\:\:\:\:\:\:\:\:$$\{\begin{array}{l}{\mathit{x}}_1-{\mathit{x}}_2=\mathit{a}\\ {\mathit{x}}_2-{\mathit{x}}_3=2\mathit{a}\\ \dots \dots \dots \dots \dots ..\\ \dots \dots \dots \dots \dots ..\\ \dots \dots \dots \dots \dots .\\ {\mathit{x}}_{\mathit{n}-1}-{\mathit{x}}_{\mathit{n}}=(\mathit{n}-1)\mathit{a}\\ {\mathit{x}}_1+{\mathit{x}}_2+\dots +{\mathit{x}}_{\mathit{n}-1}+{\mathit{x}}_{\mathit{n}}=\mathit{n}\mathit{a}\end{array}$$ \…

Question Number 9753 by j.masanja06@gmail.com last updated on 31/Dec/16 $$findthevalueofx$$$$\left(a\right)4^{2x+1}.5^{x-2}=6^{1-x}$$$$\left(b\right)4\left(3^{2x+1}\right)+17\left(3^x\right)-7=0$$ Commented by ridwan balatif last…