Question

So sánh A và B:

a. A=\(\dfrac{2011^{2011\dfrac{ }{ }}+2}{2011^{2011}-1}\)

B=\(\dfrac{2011^{2011}}{2011^{2011}-3}\)

Answer 1

\(A=\dfrac{2011^{2011}+2}{2011^{2011}-1}=\dfrac{2011^{2011}-1+3}{2011^{2011}-1}=\dfrac{2011^{2011}-1}{2011^{2011}-1}+\dfrac{3}{2011^{2011}-1}=1+\dfrac{3}{2011^{2011}-1}\left(1\right)\)

\(B=\dfrac{2011^{2011}}{2011^{2011}-3}=\dfrac{2011^{2011}-3+3}{2011^{2011}-3}=\dfrac{2011^{2011}}{2011^{2011}}+\dfrac{3}{2011^{2011}-3}=1+\dfrac{3}{2011^{2011}-3}\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow A< B\)