Question
Many junior high students have noticed that \(1=\frac{1}{3}+\frac{2}{3}=0.\bar{33}+0.\bar{66}=0.\bar{99}\). How would you use a limit to prove the same result?
▶️Answer/Explanation
\(0.\bar{99}=\lim_{x\rightarrow \infty }(1-10^{-x})=1-0=1\)
Question
Many junior high students have noticed that \(1=\frac{1}{3}+\frac{2}{3}=0.\bar{33}+0.\bar{66}=0.\bar{99}\). How would you use a limit to prove the same result?
▶️Answer/Explanation
\(0.\bar{99}=\lim_{x\rightarrow \infty }(1-10^{-x})=1-0=1\)