The 100 natural numbers 1,2,3, ·······, 100 are randomly divided into 50 groups, each group has two numbers, one of which is recorded as a, the other as B, Substituting into the algebraic formula # (189); (a + b-la-bl), we can get the result. After 50 groups are substituted, we can get 50 values, and find the minimum value of the sum of these 50 values (briefly explain the reason)

The 100 natural numbers 1,2,3, ·······, 100 are randomly divided into 50 groups, each group has two numbers, one of which is recorded as a, the other as B, Substituting into the algebraic formula # (189); (a + b-la-bl), we can get the result. After 50 groups are substituted, we can get 50 values, and find the minimum value of the sum of these 50 values (briefly explain the reason)

one thousand two hundred and seventy-five
If a > b
Then the original formula = 1 / 2 (a + B-A + b) = B
Therefore, when B = 1 ~ 50, the sum of these 50 values is the smallest
So, 1 + 2 + 3 + +50=1275