Question

So sánh

b,10¹² - 1/10¹³ - 2 và 10^{10 +} 1/10¹¹ + 1

Answer 1

Theo đầu bài ta có:
\(\hept{\begin{cases}A=\frac{10^{12}-1}{10^{13}-1}\Rightarrow10A=\frac{10^{13}-10}{10^{13}-1}=\frac{\left(10^{13}-1\right)-9}{10^{13}-1}=1-\frac{9}{10^{13}-1}\\B=\frac{10^{10}+1}{10^{11}+1}\Rightarrow10B=\frac{10^{11}+10}{10^{11}+1}=\frac{\left(10^{11}+1\right)+9}{10^{11}+1}=1+\frac{9}{10^{11}+1}\end{cases}}\)
Do \(1-\frac{9}{10^{13}-1}< 1< 1+\frac{9}{10^{11}+1}\Rightarrow10A< 10B\Rightarrow A< B\)