Question

S = \(\frac{9^{2018}+1}{9^{2017}+1}\)và M = \(\frac{9^{2017}+1}{9^{2016}+1}\)

Hãy so sánh nha !

Các bạn giúp mình nha ai nhanh mình tick cho !

Answer 1

Ta có \(\frac{1}{9S}=\frac{9^{2017}+\frac{1}{9}}{9^{2017}+1}\)=   \(\frac{9^{2017}+1-\frac{8}{9}}{9^{2017}+1}=1-\frac{\frac{8}{9}}{9^{2017}+1}\)

           \(\frac{1}{9M}=\frac{9^{2016}+\frac{1}{9}}{9^{2016}+1}\)=    \(\frac{9^{2016}+1-\frac{8}{9}}{9^{2016}+1}=1-\frac{\frac{8}{9}}{9^{2016}+1}\)

Vì \(9^{2016}+1< 9^{2017}+1\)=> \(\frac{\frac{8}{9}}{9^{2016}+1}>\frac{\frac{8}{9}}{9^{2017}+1}\)

=> \(1-\frac{\frac{8}{9}}{9^{2016}+1}< 1-\frac{\frac{8}{9}}{9^{2017}+1}\)=>  \(\frac{1}{9}S< \frac{1}{9}M\Rightarrow S< M\)