Bổ sung đề: So sánh A và B
Ta có:
A. \(2010^{1000}=\frac{1010^{1010}.2010^{1000}}{2010^{2010}}=\left(\frac{101}{201}\right)^{1010}\)
B. \(2010^{1000}=\frac{2010^{2010}.2010^{1000}}{3010^{3010}}=\left(\frac{201}{301}\right)^{3010}\)
Từ \(\frac{101}{201}>\frac{1}{2}>\frac{40401}{90601}=\left(\frac{201}{301}\right)^2\)và \(\frac{201}{301}< 1\)
có: \(\left(\frac{101}{201}\right)^{1010}>\left(\frac{201}{301}\right)^{2.1010}=\left(\frac{201}{301}\right)^{2020}>\left(\frac{201}{301}\right)^{3010}\)
Suy ra \(A=\left(\frac{101}{201}\right)^{1010}.\frac{1}{2010^{1000}}>\left(\frac{201}{301}\right)^{3010}.\frac{1}{2010^{1000}}\) hay A > B
