So sánh các số sau: C=10^123-1/10^124 và D=10^124-1/10^125-1

Đáp án:

$\begin{array}{l}
C = \dfrac{{{{10}^{123}} – 1}}{{{{10}^{124}} – 1}};D = \dfrac{{{{10}^{124}} – 1}}{{{{10}^{125}} – 1}}\\
Do:{10^{124}} – 1 < {10^{125}} – 1\\
 \Rightarrow \dfrac{{{{10}^{124}} – 1}}{{{{10}^{125}} – 1}} > \dfrac{{{{10}^{124}} – 1 – 9}}{{{{10}^{125}} – 1 – 9}}\\
 \Rightarrow \dfrac{{{{10}^{124}} – 1}}{{{{10}^{125}} – 1}} > \dfrac{{{{10}^{124}} – 10}}{{{{10}^{125}} – 10}}\\
 \Rightarrow \dfrac{{{{10}^{124}} – 1}}{{{{10}^{125}} – 1}} > \dfrac{{10\left( {{{10}^{123}} – 1} \right)}}{{10\left( {{{10}^{124}} – 1} \right)}}\\
 \Rightarrow \dfrac{{{{10}^{124}} – 1}}{{{{10}^{125}} – 1}} > \dfrac{{{{10}^{123}} – 1}}{{{{10}^{124}} – 1}}\\
 \Rightarrow D > C\\
Vậy\,C < D
\end{array}$