A= 32019-32018+32017-32016+...+33-32+3-1
3A=32020-32019+32018-32017+...+34-33+32-3
4A=32020-1
4A+1=32020
X=2020
Ta có
\(A=3^{2019}-3^{2018}+3^{2017}-3^{2016}+...+3^3-3^2+3-1\)
\(\Rightarrow3A=3^{2020}-3^{2019}+3^{2018}-3^{2016}+....+3^2-3\)
\(\Rightarrow3A+A=4A=3^{2020}-1\)
\(\Rightarrow4A+1=3^x\)
\(\Rightarrow\left(3^{2020}-1\right)+1=3^x\)
\(\Rightarrow3^{2020}=3^x\)
\(\Rightarrow x=2020\)
\(A=3^{2019}-3^{2018}+3^{2017}-2^{2016}+...+3^3-3^2+3-1\)
\(\Rightarrow3A=3^{2020}-3^{2019}+3^{2018}-3^{2017}+...+3^4-3^3+3^2-3\)
\(\Leftrightarrow3A+A=\left(3^{2020}-3^{2019}+3^{2018}-3^{2017}+...+3^4-3^3+3^2-3\right)+A\)
\(\Leftrightarrow4A=3^{2020}-1\)
\(\Leftrightarrow4A+1=3^{2020}\)
\(\Leftrightarrow x=2020\)
