According to a certain rule, arrange the number of the string: 1 / 1, 1 / 2, 2 / 2, 1 / 3, 2 / 3, 3 / 3, 1 / 4, 2 / 4, 3 / 4, 4 / 4.1/100, 2 / 100.. 100 / 100 Arrange the numbers according to a certain rule: 1 / 1, 1 / 2, 2 / 2, 1 / 3, 2 / 3, 3 / 3, 1 / 4, 2 / 4, 3 / 4, 4 / 4.1/100, 2 / 100, 3 / 100.. 99 / 100, 100 / 100. Please calculate the sum of these numbers?

According to a certain rule, arrange the number of the string: 1 / 1, 1 / 2, 2 / 2, 1 / 3, 2 / 3, 3 / 3, 1 / 4, 2 / 4, 3 / 4, 4 / 4.1/100, 2 / 100.. 100 / 100 Arrange the numbers according to a certain rule: 1 / 1, 1 / 2, 2 / 2, 1 / 3, 2 / 3, 3 / 3, 1 / 4, 2 / 4, 3 / 4, 4 / 4.1/100, 2 / 100, 3 / 100.. 99 / 100, 100 / 100. Please calculate the sum of these numbers?

two thousand five hundred and seventy-five
It is found that 1 / 1 = 1,
1/2+2/2=3/2,
1/3+2/3+3/3=2
1/4+2/4+3/4+4/4=5/2.
The result of adding numbers with the same denominator is an arithmetic sequence, with the first term of 1 and the tolerance of 0.5
So the last term = 1 + (100-1) * 0.5 = 50.5
So sum = (1 + 50.5) * 100 / 2 = 2575