Harmonic series

The harmonic series is a divergent series in the form

$\sum_{n=1}^\infty\dfrac{1}{n}=1+\frac12+\frac13+\frac14+\cdots$

It is often useful to use in comparison tests, since similar series appear fairly often. A related series is the alternating harmonic series, which takes the form

$\sum_{n=1}^\infty\dfrac{(-1)^{n-1}}{n}=1-\frac12+\frac13-\frac14+\cdots$

Unlike the harmonic series, the alternating harmonic series is convergent and converges to $\ln(2)$ .