$C$ = $1-2$ + $2^{2}$ - $2^{3}$ +..........-$2^{2011}$ + $2^{2012}$
$2C$ = $2$ - $2^{2}$ + $2^{3}$ - $2^{4}$ +........-$2^{2012}$ + $2^{2013}$
$2C+C$ =($2$ - $2^{2}$ + $2^{3}$ - $2^{4}$ +........-$2^{2012}$ + $2^{2013}$)+
($1-2$ + $2^{2}$ - $2^{3}$ +..........-$2^{2011}$ + $2^{2012}$)
$3C$=$^{2013}$ +$1$
⇔$C$ = $\frac{2^{2013} + 1}{2}$
Vậy $C$ = $\frac{2^{2013} + 1}{2}$