Finding Big O of the Harmonic Series

complexity-theory big-o time-complexity

This follows easily from a simple fact in Calculus:

enter image description here

and we have the following inequality:

enter image description here

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.


Here's a formulation using Discrete Mathematics:

enter image description here So, H(n) = O(log n)

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