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