Significantly, Oresme developed the first proof of the divergence of the harmonic series. His proof, requiring less advanced mathematics than current standard tests for divergence (for example, the integral test), begins by noting that for any n that is a power of 2, there are n /2 − 1 terms in the series between 1/(n /2) and 1/ n. Each of these terms is at least 1/ n, and since there are n /2 of them they sum to at least 1/2. For instance, there is one term 1/2, then two terms 1/3 + 1/4 that together sum to at least 1/2, then four terms 1/5 + 1/6 + 1/7 + 1/8 that also sum to at least 1/2, and so on. Thus the series must be greater than the series 1 + 1/2 + 1/2 + 1/2 + ..., which does not have a finite limit. This proves that the harmonic series must be divergent. This argument shows that the sum of the first n terms grows at least as fast as ( 1 / 2 ) log 2 ⁡ ⁡ n . (See also Harmonic series)