Category: Algebra

Question Number 5752 by Rasheed Soomro last updated on 26/May/16 $$\mathrm{Determine}$$$$1+\frac{ar}{a+r}+\frac{{ar}^2}{a+2r}+\frac{{ar}^3}{a+3r}+\dots .+\frac{{ar}^{n-1}}{a+(n-1)r}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 5742 by Rasheed Soomro last updated on 26/May/16 $$\bullet DetermineS$$$$S=a^2+ar(a+r)+{ar}^2(a+2r)+\dots +{ar}^{n-1}\{a+(n-1)r\}.$$$$$$ Answered by Yozzii last updated…

Question Number 5723 by Rasheed Soomro last updated on 25/May/16 $$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\dots .+\frac{1}{2^{\mathrm{n}}}=1-\frac{1}{2^{\mathrm{n}}}$$$$\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{the}\mathrm{above}\mathrm{for}\mathrm{integral}\mathrm{n}⩾1.$$ Commented by FilupSmith last updated on 25/May/16 $$\boldsymbol{\mathrm{LHS}}={S}=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}}+…+\frac{\mathrm{1}}{\mathrm{2}^{{n}}…

Question Number 5722 by Rasheed Soomro last updated on 25/May/16 $$\mathrm{Prove}\mathrm{by}\mathbf{mathematical}\mathbf{induction}$$$$\mathrm{that}\mathrm{tbe}\mathrm{following}\mathrm{formula}\mathrm{is}\mathrm{correct}$$$$\mathrm{for}\mathrm{all}\mathrm{positive}\mathrm{integers}\mathrm{n}:$$$$\left(\begin{array}{c}2\\ 2\end{array}\right)+\left(\begin{array}{c}3\\ 2\end{array}\right)+\left(\begin{array}{c}4\\ 2\end{array}\right)+\dots +\left(\begin{array}{c}\mathrm{n}+1\\ 2\end{array}\right)=\left(\begin{array}{c}\mathrm{n}+2\\ 3\end{array}\right)$$ Commented by Yozzii last updated on…

Question Number 71242 by TawaTawa last updated on 13/Oct/19 $$\mathrm{Given}:\frac{\mathrm{a}}{\mathrm{b}}+\frac{\mathrm{c}}{\mathrm{d}}=\frac{\mathrm{b}}{\mathrm{a}}+\frac{\mathrm{d}}{\mathrm{c}}$$$$\mathrm{Show}\mathrm{that},\frac{{\mathrm{a}}^2}{{\mathrm{b}}^2}-\frac{{\mathrm{c}}^2}{{\mathrm{d}}^2}=\frac{{\mathrm{b}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{d}}^2}{{\mathrm{c}}^2}$$ Answered by MJS…