1 / 2, 1 / 3, 1 / 4, 1 / 5... 1 / 90, 1 / 91, choose 10 numbers from them, add a sign to make the sum equal to - 1

1 / 2, 1 / 3, 1 / 4, 1 / 5... 1 / 90, 1 / 91, choose 10 numbers from them, add a sign to make the sum equal to - 1

After my careful calculation, I put together a group of numbers. - 1 / 2 - 1 / 6 - 1 / 10 - 1 / 12 - 1 / 20 - 1 / 30 - 1 / 42 - 1 / 56 - 1 / 72 - 1 / 90 = - 1. After five minutes of summary, I found a rule. Do you understand? 1 / (1 * 2) + 1 / (2 * 3) + 1 / (3 * 4) + 1 / (4 * 5) +... + 1 / (9 * 10) +