A hyperharmonic series (a.k.a. P-series) is a generalization of the harmonic series that has the form \(\sum_{n=1}^{\infty} \frac{1}{n^p}\) for some fixed real number \(p\). If you plug in \(p=1\), you get exactly the harmonic series. The demo below shows how the partial sum \(S\) of the hyperharmonic series \(\sum_{n=1}^{\infty} \frac{1}{n^{1.01}}\) grows as \(n \to \infty\). Can you tell if it converges to a number? What will that number be?