$C$ = $-2$ + $2^{2}$ - $2^{3}$ +..........-$2^{2019}$ + $2^{2020}$
$2C$ = $-2^{2}$ - $2^{3}$ + $2^{4}$ -........+$2^{2020}$ + $2^{2021}$
$2C+C$ =($-2^{2}$ - $2^{3}$ + $2^{4}$ -........+$2^{2020}$ + $2^{2021}$)+
($-2$ + $2^{2}$ - $2^{3}$ +..........-$2^{2019}$ + $2^{2020}$)
$3C$=$^{2021}$ - $2$
⇔$C$ = $\frac{2^{2021} -2}{3}$
Vậy $C$ = $\frac{2^{2021} -2}{3}$