Differences of the fraction (Posted on 2021-02-20)

The following fractions are written on the board 1/n, 2/(n-1), 3/(n-2), ... , n/1 where n is a natural number. Alice calculated the differences of the neighboring fractions in this row and found among them 10000 fractions of type 1/k (with natural k). Prove that he can find even 5000 more of such these differences.