Combining number with shape, the number axis | X-1 | + | X-2 | + | x-3 | + +|Minimum value of x-2011 |

Combining number with shape, the number axis | X-1 | + | X-2 | + | x-3 | + +|Minimum value of x-2011 |

1) |x-1 | is the distance from the point x on the number axis to the point representing 1. When x = 1, the value of |x-1 | is the smallest, and the minimum value is 0;
2) |x-1 | + |x-2 | denotes the sum of the distances from the point x on the number axis to 1 and 2: when 1 ≤ x ≤ 2, the value of|x-1 | + |x-2 | is the minimum, and the minimum value is 1;
3) | X-1 | + | X-2 | + | x-3 | represents the sum of the distances from the point x on the number axis to 1,2,3: when x = 2, the minimum value is 2;
4) | X-1 | + | X-2 | + | x-3 | + | x-4 | represents the sum of the distances from point x to 1,2,3,4 on the number axis: when 2 ≤ x ≤ 3, the minimum value is 4;
……
From this we can get the following rules
|x-1|+|x-2|+|x-3|+… +|X-2011 | when x = 1006, its value is the smallest
1005+1004+1003+1002+… +1+0+1+2+3+4+… +1005=1011030.