Harmonic Sum

The harmonic sum refers to a finite partial sum of the harmonic series. It is defined as:

$$H_n=\sum _{k=1}^n\frac{1}{k}$$

Integral Representation

The harmonic sum can be represented using an integral of a geometric series:

$$H_n={\int }_0^1(1+x+x^2+\cdots +x^{n-1})dx={\int }_0^1\frac{1-x^n}{1-x}dx$$