The harmonic series is \[1+\frac12+\frac13+\frac14+\cdots\]
The sum of the first \(n\) terms of this series lies between \(\ln n\) and \(1+\ln n\), but there is no simple formula for the sum.
The infinite harmonic series diverges: \[\sum_{n=1}^\infty \frac{1}{n} = \infty.\]
