根据微积分中的一个简单事实，很容易做到这一点:

This follows easily from a simple fact in Calculus:

我们有以下不等式:

在这里我们可以得出结论，S = 1 + 1/2 + ... + 1/n都是Ω(log(n))和O(log(n))，因此它是Ɵ(log(n) )，实际上边界是紧密的.

Here we can conclude that S = 1 + 1/2 + ... + 1/n is both Ω(log(n)) and O(log(n)), thus it is Ɵ(log(n)), the bound is actually tight.