In the sequence 1 / 2,1 / 3,2 / 3,1 / 4,2 / 4,3 / 4,1 / 5 What is 78 / 99? Find the sum of the first 100 items

In the sequence 1 / 2,1 / 3,2 / 3,1 / 4,2 / 4,3 / 4,1 / 5 What is 78 / 99? Find the sum of the first 100 items

There is one number with 2 as the denominator
3 2
.
.
.
98 97
Then 78 / 99 is the first + 2 + 3 +. + 97 + 78 = 1 / 2 x 97 (1 + 97) + 78 = 4831
According to the summation formula n (n + 1) / 2 = 100, we can know that the denominator of the 100th term is 15 and the numerator is 9
Numbers with denominator 2 add up to 1 / 2
The denominator is 3.1
4 3/2
5 2
6 5/2
.
14 13/2
The sum of the first 100 items is (1 / 2 + 13 / 2) × 13 × 1 / 2 + (1 / 2) (1 + 9) 9 / 15 = 48.5
I don't know if you learn arithmetic series