A simple algorithm for an arithmetic problem 1 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56 = how much Russia

A simple algorithm for an arithmetic problem 1 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56 = how much Russia

1 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56 = 1 + (1 / 2-1 / 3) + (1 / 3-1 / 4) + (1 / 4-1 / 5) + (1 / 5-1 / 6) + (1 / 6-1 / 7) + (1 / 7-1 / 8) = 1 + 1 / 2-1 / 3 + 1 / 3-1 / 4 + 1 / 4-1 / 5 + 1 / 5-1 / 6-1 / 7 + 1 / 7-1 / 8 = 1 + 1 / 2-1 / 8 = 1 + 3 / 8