Category: Algebra

Question Number 162265 by HongKing last updated on 28/Dec/21 $$\mathrm{Calculate}:\underset{\mathbf{k}=1}{\sum ^{\mathrm{\infty }}}\frac{{\mathrm{H}}_{2\mathbf{k}}{(-1)}^{\mathbf{k}-1}}{2\mathrm{k}+1}$$$$\mathrm{where},{\mathrm{H}}_{\mathbf{n}}\mathrm{is}\mathrm{the}\mathrm{n}-\mathrm{th}\mathrm{harmonic}\mathrm{number}$$ Terms of Service Privacy Policy Contact:…

Question Number 31194 by U Htay KyawMyint last updated on 03/Mar/18 $$Findtheremainderwhen{x}^{203}-1$$$$isdividedby{x}^4-1.$$ Commented by 6123 last updated on 04/Mar/18…

Question Number 162261 by mr W last updated on 28/Dec/21 $$find\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{5^n-1}=?$$$$orgenerally$$$$\mathrm{\Phi }\left(k\right)=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{k^n-1}=?withk\in N,k⩾2$$ Commented by…

Question Number 96715 by bobhans last updated on 04/Jun/20 $$\mathrm{find}\mathrm{real}\mathrm{solution}\mathrm{of}\mathrm{equation}$$$$x^5+x^4+1=0$$ Answered by bemath last updated on 04/Jun/20 $$\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left({x}^{\mathrm{3}}…

Question Number 96650 by bobhans last updated on 03/Jun/20 $$\mathrm{solve}2\sqrt[3]{2\mathrm{y}-1}={\mathrm{y}}^3+1$$ Answered by john santu last updated on 03/Jun/20 $$\sqrt[3]{2\mathrm{y}-1}=\frac{{\mathrm{y}}^3+1}{2}$$$$\Rightarrow\mathrm{f}^{−\mathrm{1}}…