Question

A=\(\dfrac{100^{10+1}}{100^{10-1}}\)và B=\(\dfrac{100^{10-1}}{100^{10-3}}\)

Answer 1

Ta có :

\(A=\dfrac{100^{10}+1}{100^{10}-1}=\dfrac{100^{10}-1+2}{100^{10}-1}=\dfrac{100^{10}-1}{100^{10}-1}+\dfrac{2}{100^{10}-1}=1+\dfrac{2}{100^{10}-1}\)

\(B=\dfrac{100^{10}-1}{100^{10}-3}=\dfrac{100^{10}-3+2}{100^{10}-3}=\dfrac{100^{10}-3}{100^{10}-3}+\dfrac{2}{100^{10}-3}=1+\dfrac{2}{100^{10}-3}\)

\(\) Vì \(1+\dfrac{2}{100^{10}-1}< 1+\dfrac{2}{100^{10}-3}\Rightarrow A< B\)