> 1/8 = 0.1 + 0.02 + 0.004 + 0.0008 + ... The sum of a convergent series is a / (1 - r) where a is the first value, and r is the ratio between the n+1th and nt

> 1/8 = 0.1 + 0.02 + 0.004 + 0.0008 + ... The sum of a convergent series is a / (1 - r) where a is the first value, and r is the ratio between the n+1th and nth term. a = 1/10, r = 1/5 n = (1 / 10) / (1 - (1 / 5)) n = (1 / 10) / (4 / 5) n = 5 / 40 n = 1 / 8