Question

So sánh: \(A=\frac{2009^{2017}+1}{2009^{2016}+1}\) và \(B=\frac{2009^{2018}-2}{2009^{2017}-2}\)

Answer 1

Ta có : 

\(\frac{1}{2009}A=\frac{2009^{2017}+1}{2009^{2017}+2009}=\frac{2009^{2017}+2009}{2009^{2017}+2009}-\frac{2008}{2009^{2017}+2009}=1-\frac{2008}{2009^{2017}+2009}< 1\)

\(\frac{1}{2009}B=\frac{2009^{2018}-2}{2009^{2018}-4018}=\frac{2009^{2018}-4018}{2009^{2018}-4018}+\frac{4016}{2009^{2018}-4018}=1+\frac{4016}{2009^{2018}-4018}>1\)

\(\Rightarrow\)\(A< 1< B\)

Vậy \(A< B\)

Chúc bạn học tốt ~ 

Answer 2

Vi 2009^2017 + 1 / 2009^2016 + 1 > 1

nen 2009^2018 + 1 / 2009^2016 + 1 < 2009^2018 + 1 - 3 / 2009^2016 + 1 - 3 = 2009^2018 - 2 / 2009^2017 - 2

Vay ...

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