Series

Harmonic Series

Needed to be familiar with this concept for this codeforces problem https://codeforces.com/problemset/problem/1996/D to prove that we can find $b$ in a reasonable time

In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: $\sum _{n=1}^{\infty }\frac{1}{n}=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\cdots$

It is a divergent series.

The first $N$ terms of the series sums to approximately ${\sum }_{n=1}^N\frac{1}{n}\approx \ln N+\frac{1}{2N}+\gamma$ where

• $\gamma \approx 0.577$