Question

tìm x biết: (x + \(\frac{1}{2}\)) + (x + \(\frac{1}{4}\)) + (x +\(\frac{1}{8}\) ) + ... + (x + \(\frac{1}{512}\)) = 1

Answer 1

\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+...+\left(x+\frac{1}{512}\right)=1\)

\(9x+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}\right)=1\)

\(9x+\left[\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+....+\left(\frac{1}{256}-\frac{1}{512}\right)\right]=1\)

\(9x+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{512}\right)=1\)

\(9x+\left(1-\frac{1}{512}\right)=1\)

\(9x+\frac{511}{512}=1\)

\(9x=1-\frac{511}{512}\)

\(9x=\frac{1}{512}\)

\(\Rightarrow x=\frac{1}{512}\div9=\frac{1}{4608}\)