$A=2019^{9}+2019^{10}$ và $B=2020^{10}$
Ta có:
`\frac{A}{B}=\frac{2019^{9}+2019^{10}}{2020^{10}`
`⇔\frac{A}{B}=\frac{2019^{9}+2019^{9}.2019}{2020^{9}.2020}`
`⇔\frac{A}{B}=\frac{2019^{9}.(1+2019)}{2020^{9}.2020}`
`⇔\frac{A}{B}=\frac{2019^{9}.2020}{2020^{9}.2020}`
`⇔\frac{A}{B}=\frac{2019^{9}}{2020^{9}}`
Vì $2019^{9}<2020^{9}$
$⇒2019^{9}+2019^{10}<2020^{10}$
$⇒A<B$