Question

Sosánh: M=  5^2018+1/5^2017+1 và N=5^2017+1/5^2016+1

Answer 1

`M=(5^2018+1)/(5^2017+1)`

`1/5M=(5^2017+1/5)/(5^2017+1)`

`1/5M=1-(4/5)/(5^2017+1)`

Tương tự:

`1/5N=1-(4/5)/(5^2016+1)`

`5^2017+1>5^2016+1`

`=>(4/5)/(5^2017+1)<(4/5)/(5^2016+1)`

`=>1-(4/5)/(5^2017+1)>1-(4/5)/(5^2016+1)`

`=>1/5M>1/5N=>M>N`

Answer 2

\(M=\dfrac{5^{2018}+1}{5^{2017}+1}=5-\dfrac{4}{5^{2017}+1}\)

\(N=\dfrac{5^{2017}+1}{5^{2016}+1}=5-\dfrac{4}{5^{2016}+1}\)

mà \(-\dfrac{4}{5^{2017}+1}>-\dfrac{4}{5^{2016}+1}\)

nên M>N