Occurrences of Grandi's series

Grandi's series is a mathematical series defined as: \[ S = 1 - 1 + 1 - 1 + 1 - 1 + \ldots \] The series can be rewritten in summation notation as: \[ S = \sum_{n=0}^{\infty} (-1)^n \] This series does not converge in the traditional sense, as its partial sums oscillate between 1 and 0.