Category: Algebra

Question Number 6535 by Temp last updated on 01/Jul/16 $$\underset{x=1}{\sum ^{\mathrm{\infty }}}\frac{1}{x}=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\dots$$$$\mathbf{Is}\mathbf{the}\mathbf{following}\mathbf{true}?$$$$\therefore \mathrm{\Sigma }\frac{1}{x}=\mathrm{\Sigma }(\frac{1}{2x}+\frac{1}{2x-1})$$$$=\mathrm{\Sigma }\left(\frac{2x-1+2x}{2x(2x-1)}\right)$$$$=\mathrm{\Sigma }\left(\frac{2x-2+1+2x}{2x(2x-1)}\right)$$$$=\mathrm{\Sigma }(\frac{4x-2}{2x(2x-1)}+\frac{1}{2x(2x-1)})$$$$=\Sigma\left(\frac{\mathrm{2}\left(\mathrm{2}{x}−\mathrm{1}\right)}{\mathrm{2}{x}\left(\mathrm{2}{x}−\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{2}{x}\left(\mathrm{2}{x}−\mathrm{1}\right)}\right) \…

Question Number 137588 by bramlexs22 last updated on 04/Apr/21 $$Forapositivenumbern,let$$$$f\left(n\right)bethevalueof$$$$f\left(n\right)=\frac{4n+\sqrt{4n^2-1}}{\sqrt{2n+1}+\sqrt{2n-1}}$$$$calculatef\left(1\right)+f\left(2\right)+f\left(3\right)+\dots +f\left(40\right).$$ Answered by bemath last updated on…

Question Number 137584 by bramlexs22 last updated on 04/Apr/21 $$Given\{\begin{array}{l}{a}_{2n}=a_n.a_2+1\\ a_{2n+1}=a_n.a_2-2\end{array}and$$$$\{\begin{array}{l}{a}_7=2\\ 0<a_1<1\end{array}.Find{a}_{25}=?$$$$$$…

Question Number 137563 by liberty last updated on 04/Apr/21 $$let\frac{x^2+y^2}{x^2-y^2}+\frac{x^2-y^2}{x^2+y^2}=k$$$${find}\:{the}\:{value}\:{of}\:\frac{{x}^{\mathrm{8}} +{y}^{\mathrm{8}} }{{x}^{\mathrm{8}} −{y}^{\mathrm{8}} }+\frac{{x}^{\mathrm{8}} −{y}^{\mathrm{8}}…

Question Number 6476 by sanusihammed last updated on 28/Jun/16 Answered by Rasheed Soomro last updated on 28/Jun/16 $$Givenequation:x^2-px+8=0$$$$Sumoftheroots=-\frac{coefficientofx}{coefficientof{x}^2}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=−\frac{−{p}}{\mathrm{1}}={p} \…