$$999\,\frac{1}{7} + 999\frac{2}{7} + 999\frac{3}{7} + $$     $$999\frac{4}{7} + $$   $$999\frac{5}{7} + $$   $$999\frac{6}{7}$$   is simplified to-

$$999\,\frac{1}{7} + 999\frac{2}{7} + 999\frac{3}{7} + $$     $$999\frac{4}{7} + $$   $$999\frac{5}{7} + $$   $$999\frac{6}{7}$$
$$ \Rightarrow \left( {999 \times 6} \right) + $$   $$\left( {\frac{1}{7} + \frac{2}{7} + \frac{3}{7} + \frac{4}{7} + \frac{5}{7} + \frac{6}{7}} \right)$$
$$\eqalign{ & \Rightarrow 5994 + \left( {\frac{{21}}{7}} \right) \cr & \Rightarrow 5994 + 3 \cr & \Rightarrow 5997 \cr} $$