Category: Algebra

Question Number 157120 by cortano last updated on 20/Oct/21 $$\underset{n=0}{\sum ^{\mathrm{\infty }}}\left(\frac{1}{(3n+1)(3n+2)}\right)=?$$ Answered by puissant last updated on 20/Oct/21 $$\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}\right)=\frac{\mathrm{1}}{\mathrm{9}}\underset{{n}=\mathrm{0}} {\overset{\infty}…

Question Number 26042 by sanjib bibhar last updated on 18/Dec/17 $${ax}^2-bx=0$$ Commented by sanjib bibhar last updated on 19/Dec/17 $$thanks$$…

Question Number 157080 by amin96 last updated on 19/Oct/21 Commented by cortano last updated on 20/Oct/21 $$\Rightarrow 1+\frac{1-\cos 2x}{2}=\frac{3\sin 2x}{2}$$$$\Rightarrow 3-\cos 2x=3\sin 2x$$$$\Rightarrow 3-\cos 2x=3\sqrt{1-\cos {}^2\left(2x\right)}$$$$\Rightarrow\mathrm{9}+\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)−\mathrm{6cos}\:\left(\mathrm{2}{x}\right)=\mathrm{9}−\mathrm{9cos}\:^{\mathrm{2}}…

Question Number 157057 by amin96 last updated on 19/Oct/21 $$\frac{1}{7}+\frac{1}{13}+\frac{1}{19}=a$$$$find\frac{2}{7}+\frac{4}{13}+\frac{6}{19}=?$$ Commented by aliyn last updated on 19/Oct/21 $$\frac{2}{7}+\frac{4}{13}+\frac{6}{19}=(\frac{2}{7}+\frac{2}{13}+\frac{2}{19})+(\frac{2}{13}+\frac{4}{19})$$$$ \…

Question Number 157044 by MathSh last updated on 18/Oct/21 $$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$$$(\sin 2\mathbf{x}+{4\cos }^2\mathbf{x}+1)(\cos 5\mathbf{x}-\cos \mathbf{x})<0$$ Answered by mindispower last updated on 19/Oct/21 $$1+sin\left(2x\right)={(sin\left(x\right)+cos\left(x\right))}^2$$$$\Leftrightarrow\left(\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)^{\mathrm{2}}…