Ответ: 1346.

Решение:

Имеем:

$\displaystyle \left(\frac{1 + 2}{3} + \frac{4 + 5}{6} + \frac{7 + 8}{9} + \ldots + \frac{2017 + 2018}{2019}\right) + \left(1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{673}\right) = $

$\displaystyle = \left(\frac{(3 − 2) + (3 − 1)}{3} + \frac{(6 − 2) + (6 − 1)}{6} + \frac{(9 − 2) + (9 − 1)}{9} + \ldots \right.$

$\displaystyle \left. \ldots + \frac{(2019 − 2) + (2019 − 1)}{2019}\right) + \left(1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{673}\right) = $

$\displaystyle = \left(\frac{(3 + 3) − (2 + 1)}{3} + \frac{(6 + 6) − (2 + 1)}{6} + \frac{(9 + 9) − (2 + 1)}{9} + \ldots \right. $

$\displaystyle \left. \ldots + \frac{(2019 + 2019) − (2 + 1)}{2019}\right) + \left(1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{673}\right) = $

$\displaystyle = \left(2 − \frac{3}{3} + 2 − \frac{3}{6} + 2 − \frac{3}{9} + \ldots + 2 − \frac{3}{2019}\right) + \left(1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{673}\right) = $

$\displaystyle = 2⋅673 − \left(1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{673}\right) + \left(1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{673}\right) = $

$ = 2⋅673 = 1346$.