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 150918 by mathdanisur last updated on 16/Aug/21

Commented by puissant last updated on 16/Aug/21

$$=\left[\frac{\underset{k=0}{\sum ^{1995}}{2}^k}{1997}\right]$$$$=\frac{1}{1997}\left(\frac{1-2^{1996}}{1-2}\right)$$$$=\frac{1}{1997}(2^{1996}-1)$$$$=\frac{2^{1996}-1}{1997}★$$

Commented by mathdanisur last updated on 16/Aug/21

$$\mathrm{is}\mathrm{a}\mathrm{full}\mathrm{part}\mathrm{purchase}\mathrm{operation}$$

Answered by nimnim last updated on 16/Aug/21

$$=\left(\frac{2^0}{1997}\right)+\left(\frac{2^1}{1997}\right)+\left(\frac{2^2}{1997}\right)+...+\left(\frac{2^{1995}}{1997}\right)$$$$=\frac{1}{1997}\left(\frac{2^{1996}-1}{2-1}\right),\mathrm{a}=1,\mathrm{r}=2>1,\mathrm{sum}\mathrm{of}\mathrm{gp}$$$$=\frac{2^{1996}-1}{1997}★$$$$\mathrm{PS}:\mathrm{I}\mathrm{dont}\mathrm{understand}\mathrm{how}-998\mathrm{appeared}.$$$$\mathrm{Maybe},\mathrm{I}\mathrm{used}\mathrm{the}\mathrm{wrong}\mathrm{method}\mathrm{or}$$$$\mathrm{you}\mathrm{give}\mathrm{the}\mathrm{wrong}\mathrm{answer}!$$

Commented by mr W last updated on 16/Aug/21

$$\left[x\right]=greatestintegerequaltoorless$$$$thanx.$$$$\left[\frac{1}{1997}\right]=0$$$$\left[\frac{2}{1997}\right]=0$$$$...$$$$\left[\frac{2^{10}}{1997}\right]=0$$$$\left[\frac{2^{11}}{1997}\right]=1$$$$\left[\frac{2^{12}}{1997}\right]=2$$$$...$$

Answered by maged last updated on 16/Aug/21

$$\frac{2^{1996}-1}{1997}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com