Ta có:.
`A=1-2+2^2 -2^3 +...+2^{2018}-2^{2019}`
`=>2A=2-2^2+2^3 -2^4 +...+2^{2019}-2^{2020}`
`=>A+2A=(1-2+2^2 -2^3 +...+2^{2018}-2^{2019})+(2-2^2+2^3 -2^4 +...+2^{2019}-2^{2020})`
`=>3A=1-2^{2020}`
Theo đề bài:
`\qquad 1-3A=2^x`
`=>1-(1-2^2020)=2^x`
`=>1-1+2^{2020}=2^x`
`=>2^{2020}=2^x`
`=>x=2020`
Vậy $x=2020$