So sánh A và B biết A = \(\frac{{{{10}^{2020}} + 1}}{{{{10}^{2021}} + 1}}\) và B = \(\frac{{{{10}^{2021}} + 1}}{{{{10}^{2022}} + 1}}\).

10A = \[\frac{{10.\left( {{{10}^{2020}} + 1} \right)}}{{{{10}^{2021}} + 1}} = \frac{{{{10}^{2021}} + 10}}{{{{10}^{2021}} + 1}} = 1 + \frac{9}{{{{10}^{2021}} + 1}}\]

10B = \[\frac{{10.\left( {{{10}^{2021}} + 1} \right)}}{{{{10}^{2022}} + 1}} = \frac{{{{10}^{2022}} + 10}}{{{{10}^{2022}} + 1}} = 1 + \frac{9}{{{{10}^{2022}} + 1}}\]

Vì \[\frac{9}{{{{10}^{2021}} + 1}} > \frac{9}{{{{10}^{2022}} + 1}}\] nên \[1 + \frac{9}{{{{10}^{2021}} + 1}} > 1 + \frac{9}{{{{10}^{2022}} + 1}}\]

Nên 10A > 10B hay A > B.