\(\frac{2^{2019}+1}{2^{2020}+1}< 1\Rightarrow\frac{2^{2019}+1}{2^{2020}+1}< \frac{2^{2019}+\left(1+1\right)}{2^{2020}+\left(1+1\right)}\\ \Rightarrow B< \frac{2^{2019}+2}{2^{2020}+2}\\ \Rightarrow B< \frac{2\left(2^{2018}+1\right)}{2\left(2^{2019}+1\right)}\\ \Rightarrow B< \frac{2^{2018}+1}{2^{2019}+1}\\ \Rightarrow B< A\\ \Rightarrow A>B\left(đpcm\right)\)
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22019+122020+1<1⇒22019+122020+1<22019+(1+1)22020+(1+1)⇒B<22019+222020+2⇒B<2(22018+1)2(22019+1)⇒B<22018+122019+1⇒B<A⇒A>B(đpcm)
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