The alternating harmonic series is a modification on the harmonic series in which the terms have alternating signs (+ - + - + …). We write it as \(\sum_{n=1}^{\infty} (-1)^{n-1} \frac{1}{n}\) where the power of \((-1)\) is used to express the alternating sign. The demo below shows how the partial sum \(S\) grows as \(n \to \infty\). Can you tell if it converges to a number? And what will that number be?