Question

So sánh : \(A=\dfrac{2019^{2020}+1}{2019^{2019}-1}\) và \(B=\dfrac{2019^{2019}+1}{2019^{2018}-1}\) 

Answer 1

Lời giải:

Ta có: 

\(A+1=\frac{2019^{2019}+2019^{2020}}{2019^{2019}-1}=\frac{2019^{2019}.2020}{2019^{2019}-1}\)

\(B+1=\frac{2019^{2019}+2019^{2018}}{2019^{2018}-1}=\frac{2019^{2018}.2020}{2019^{2018}-1}\) \(=\frac{2019^{2019}.2020}{2019^{2019}-2019}>\frac{2019^{2019}.2020}{2019^{2019}-1}\)

$\Rightarrow B+1>A+1$

$\Rightarrow B>A$