Question

[Khánh Xuân]

1. So sánh A và B biết : A = \(\frac{2019^{2019}+1}{2019^{2020}+1}\)        ; B =\(\frac{2019^{2018}+1}{2019^{2019}+1}\)

2.So sánh M và N biết: M = \(\frac{100^{100}+1}{100^{99}+1}\)            ; N= \(\frac{100^{101}+1}{100^{100}+1}\)

Hiện tại mình đang cần gấp giúp mk nha!

Answer 1

[zZz Cool Kid_new zZz]

1

\(A=\frac{2019^{2019}+1}{2019^{2020}+1}< \frac{2019^{2019}+1+2018}{2019^{2020}+1+2018}=\frac{2019^{2019}+2019}{2019^{2020}+2019}=\frac{2019\left(2019^{2018}+1\right)}{2019\left(2019^{2019}+1\right)}\)

\(=\frac{2019^{2018}+1}{2019^{2019}+1}\)

Answer 2

[zZz Cool Kid_new zZz]

2

\(M=\frac{100^{101}+1}{100^{100}+1}< \frac{100^{101}+1+99}{100^{100}+1+99}=\frac{100^{101}+100}{100^{100}+100}=\frac{100\left(100^{100}+1\right)}{100\left(100^{99}+1\right)}\)

\(=\frac{100^{100}+1}{100^{99}+1}=N\)