Question

So sánh:

a)A=\(\frac{10^{15}+1}{10^{16}+1}\),B=\(\frac{10^{16}+1}{10^{17}+1}\)

b)C=\(\frac{10^{1992}+1}{10^{1991}+1}\),D=\(\frac{10^{1993}+1}{10^{1992}+1}\)

Answer 1

a) Ta có: \(10A=\frac{10^{16}+10}{10^{16}+1}=1+\frac{9}{10^{16}+1}\)

\(10B=\frac{10^{17}+10}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)

\(\frac{9}{10^{16}+1}>\frac{9}{10^{17}+1}\Rightarrow1+\frac{9}{10^{16}+1}>1+\frac{9}{10^{17}+1}\)

\(\Rightarrow10A>10B\)

\(\Rightarrow A>B\)

Vậy A > B

b) Ta có: \(\frac{1}{10}C=\frac{10^{1992}+1}{10^{1992}+10}=1+\frac{10^{1992}+1}{9}\)

\(\frac{1}{10}D=\frac{10^{1993}+1}{10^{1993}+10}=1+\frac{10^{1993}+1}{9}\)

\(\frac{10^{1992}+1}{9}< \frac{10^{1993}+1}{9}\Rightarrow1+\frac{10^{1992}+1}{9}< 1+\frac{10^{1993}+1}{9}\)

\(\Rightarrow\frac{1}{10}C< \frac{1}{10}D\)

\(\Rightarrow C< D\)

Vậy C < D