 Grandi's series

The series with terms $a_n=(-1{)}^n$, indexed from zero, named for Guido Grandi. Its even-indexed partial sums are one and its odd-indexed partial sums are zero, so it has no ordinary sum. First-order Cesàro summation gives $1/2$. Grouping adjacent pairs would obscure this distinction: the partial sums of the grouped expressions select only one of the original subsequences.

Grandi's series is an infinite series defined as follows: \[ S = 1 - 1 + 1 - 1 + 1 - 1 + \ldots \] It alternates between 1 and -1 indefinitely.