Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 145499 by mathdanisur last updated on 05/Jul/21

$$\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+...-\frac{1}{256}=\frac{\mathit{z}+1}{256}$$$$find\mathit{z}=?$$

Answered by gsk2684 last updated on 05/Jul/21

$$\mathrm{sum}\mathrm{of}8\mathrm{terms}\mathrm{in}\mathrm{G}.\mathrm{P}.$$$$\frac{1}{2}\left(\frac{1-{(-\frac{1}{2})}^8}{1-(-\frac{1}{2})}\right)=\frac{84+1}{256}$$

Commented by mathdanisur last updated on 05/Jul/21

$$thanksSercool$$

Answered by Ar Brandon last updated on 05/Jul/21

$$\mathrm{S}=-\underset{\mathrm{n}=1}{\sum ^8}{(-\frac{1}{2})}^{\mathrm{n}}=-\frac{-\frac{1}{2}(1-{(-\frac{1}{2})}^8)}{1-(-\frac{1}{2})}$$$$=\frac{\frac{1}{2}(1-\frac{1}{256})}{\frac{3}{2}}=\frac{1}{3}\left(\frac{255}{256}\right)=\frac{\mathrm{z}+1}{256}$$$$\Rightarrow \mathrm{z}=\frac{255}{3}-1=\frac{252}{3}=84$$

Commented by mathdanisur last updated on 05/Jul/21

$$thanksSercool$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com