Grandi's series
= Grandi's series
{c}
{title2=$1-1+1-1+\cdots$}
{wiki}
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>.