Question

so sánh

A= \(\frac{2^{10}+1}{2^{10}-1}\) và B=\(\frac{2^{10}-1}{2^{10}-3}\)

Answer 1

Ta có: \(A=\frac{2^{10}+1}{2^{10}-1}=\frac{2^{10}-1+2}{2^{10}-1}=1+\frac{2}{2^{10}-1}\)(1)

\(B=\frac{2^{10}-1}{2^{10}-3}=\frac{2^{10}-3+2}{2^{10}-3}=1+\frac{2}{2^{10}-3}\)(2)

Ta có: \(2^{10}-1>2^{10}-3\)

\(\Rightarrow\frac{2}{2^{10}-1}< \frac{2}{2^{10}-3}\)

hay \(1+\frac{2}{2^{10}-1}< 1+\frac{2}{2^{10}-3}\)(3)

Từ (1), (2) và (3) suy ra A<B