6. Given that $a$, $b$, and $c$ are integers, and $a+b=2006$, $c-a=2005$. If $a<b$, then the maximum value of $a+b+c$ is $\qquad$
II, 6.5 013.
From $a+b=2006, c-a=2005$, we get $a+b+c=a+4011$.
Since $a+b=2006(a<b, a$ is an integer $)$, therefore, the maximum value of $a$ is 1002.
Thus, the maximum value of $a+b+c$ is 5013.