Let denote the -th harmonic number. Prove that

**Solution**

We recall the series . Integrating we get

The last takes the form

where denotes the dilogarithm function. Thus,

A site of university mathematics

Home » Uncategorized » Harmonic series

Let denote the -th harmonic number. Prove that

**Solution**

We recall the series . Integrating we get

The last takes the form

where denotes the dilogarithm function. Thus,