Ta có:
$D = -1 - 2^{2} - 2^{3} - ... - 2^{2018} = -1 - 2^{2} - \left ( 2^{3} + 2^{4} + ... + 2^{2018} \right )$
$\Rightarrow -2.D = 2 + 2^{3} + 2^{4} + ... + 2^{2019} = 2 + 2^{2019} + \left ( 2^{3} + 2^{4} + ... + 2^{2018} \right )$
Suy ra $-D = -2D + D = 2 + 2^{2019} + \left ( 2^{3} + 2^{4} + ... + 2^{2018} \right ) - 1 - 2^{2} - \left ( 2^{3} + 2^{4} + ... + 2^{2018} \right )$
$\Rightarrow -D = \left ( 2 + 2^{2019} - 1 - 2^{2} \right ) + \left [ \left ( 2^{3} + 2^{4} + ... + 2^{2018} \right ) - \left ( 2^{3} + 2^{4} + ... + 2^{2018} \right ) \right ]$
$\Rightarrow -D = 2 + 2^{2019} - 1 - 2^{2}$
$\Rightarrow -D = -3 + 2^{2019}$
$\Rightarrow D = 3 - 2^{2019}$