Question

Tìm x biết  (x+1/2) + (x+1/4) + (x+1/8) + (x+1/16) = 1

Answer 1

\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)

\(\Rightarrow\left(x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=1\)

\(\Rightarrow4x+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}\right)=1\)

\(\Rightarrow4x+1-\frac{1}{16}=1\)

\(\Rightarrow4x=1-1+\frac{1}{16}=\frac{1}{16}\)

\(\Rightarrow x=\frac{1}{16}:4=\frac{1}{64}\)

vậy \(x=\frac{1}{64}\)