1 / 1 + 1 / 2 + ... + 1 / 100 =
1 × 100 / 1 + 2 + ... + 100 =
100 / 100 × 101 : 2 =
100 / 10100 : 2 =
100 / 5050 =
10 / 505 = 2 / 101