Question

      So sánh A và B                           \(A=\frac{10^{234}+1}{10^{235}+1}\)     Và          \(B=\frac{10^{235}+1}{10^{236}+1}\)

Answer 1

Ta có:

\(10A=10.\left(\frac{10^{234}+1}{10^{235}+1}\right)=\frac{10^{235}+10}{10^{235}+1}=\frac{10^{235}+1}{10^{235}+1}+\frac{9}{10^{235}+1}=1+\frac{9}{10^{235}+1}\)

\(10B=10.\left(\frac{10^{235}+1}{10^{236}+1}\right)=\frac{10^{236}+10}{10^{236}+1}=\frac{10^{236}+1}{10^{236}+1}+\frac{9}{10^{236}+1}=1+\frac{9}{10^{236}+1}\)

\(10^{235}+1<10^{236}+1\Rightarrow\frac{9}{10^{235}+1}\)\(>\)\(\frac{9}{10^{236}+1}\)

\(\Rightarrow1+\frac{9}{10^{235}+1}\)\(>\)\(1+\frac{9}{10^{236}+1}\)

\(\Rightarrow10A>10B\)

\(\Rightarrow A>B\)

Vậy \(A>B\)