Question

So Sánh:

\(\dfrac{2018^{2018}}{2019^{2019}}\) và \(\dfrac{2018^{2018}+2018}{2019^{2019}+2019}\)

ai giúp với tks nhìu

Answer 1

Lời giải:

Ta có:

\(2018^{2018}(2019^{2019}+2019)=2018^{2018}.2019^{2019}+2018^{2018}.2019<2018^{2018}.2019^{2019}+2019^{2018}.2019 \)

\(< 2018^{2018}.2019^{2019}+2019^{2019}.2018\)

\(\Leftrightarrow 2018^{2018}(2019^{2019}+2019)< 2019^{2019}(2018^{2018}+2018)\)

\(\Rightarrow \frac{2018^{2018}}{2019^{2019}}< \frac{2018^{2018}+2018}{2019^{2019}+2019}\)