Question

So sánh A với B :

A=2009^2008-1/2009^2009-1

B=2009^2007+1/2009^2008+1

trình bày ra nhé ^-^

Answer 1

Ta có: \(A=\frac{2009^{2008}-1}{2009^{2009}-1}\Rightarrow2009A=\frac{2009^{2009}-2009}{2009^{2009}-1}=1-\frac{2008}{2009^{2009}-1}\)

\(B=\frac{2009^{2007}+1}{2009^{2008}+1}\Rightarrow2009B=\frac{2009^{2008}+2009}{2009^{2008}+1}=1+\frac{2008}{2009^{2008}+1}\)

Vì \(\frac{2008}{2009^{2009}-1}< \frac{2008}{2^{2008}+1}\Rightarrow1-\frac{2008}{2009^{2009}-1}< 1+\frac{2009}{2009^{2008}+1}\)

\(\Rightarrow2009A< 2009B\)

\(\Rightarrow A< B\)

Vậy A < B

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Answer 2

help me

Answer 3

Ta có :

A = \(\dfrac{2009^{2008}-1}{2009^{2009}-1}\) = \(\dfrac{2009^{2008}-1}{2009.2009^{2008}-1}\) = \(\dfrac{-1}{-2009}\) = \(\dfrac{1}{2009}\)

B = \(\dfrac{2009^{2007}+1}{2009^{2008}+1}\) = \(\dfrac{2009^{2007}+1}{2009.2009^{2007}+1}\) = \(\dfrac{1}{2009}\)

Vì : \(\dfrac{1}{2009}\) = \(\dfrac{1}{2009}\) nên A = B

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