Question

sa sánh C= 2018^2011+1/ 2018^2019 +1 và D= 2018^2017 /2018^2013 +1

Answer 1

C = \(\dfrac{2018^{2011}+1}{2018^{2019}+1}\)

2018²⁰¹¹ < 2018²⁰¹⁹ ⇒ 2018²⁰¹¹ + 1 < 2018²⁰¹⁹ + 1

⇒ C < 1

D = \(\dfrac{2018^{2017}}{2018^{2013}+1}\) 

Tử số D = 2018²⁰¹⁷ = 2018²⁰¹⁶.( 2017 + 1)

              = 2018²⁰¹⁶.2017 + 2018²⁰¹⁶ > 2018²⁰¹³ + 1

D > 1

Vì C < 1 < D 

Vậy C < D

 

 

Answer 2

\(C=2018^{2011}+\dfrac{1}{2018^{2019}+1}\)

\(D=\dfrac{2018^{2017}}{2018^{2013}+1}=\dfrac{2018^{2013}.2018^4}{2018^{2013}+1}=\dfrac{\left(2018^{2013}+1-1\right).2018^4}{2018^{2013}+1}=2018^4-\dfrac{2018^4}{2018^{2013}+1}\)

mà \(2018^4< 2018^{2011}\)

\(\Rightarrow D=2018^4-\dfrac{2018^4}{2018^{2013}+1}< 2018^{2011}-\dfrac{2018^4}{2018^{2013}+1}\)

mà \(2018^{2011}-\dfrac{2018^4}{2018^{2013}+1}< C=2018^{2011}+\dfrac{1}{2018^{2019}+1}\)

\(\Rightarrow D< C\)