A means of summing series which generalizes the usual definition of convergence. Given a series ${\displaystyle \sum }_1^{\infty }{a}_k$ then define $s_n={\displaystyle \sum }_1^n{a}_k$. The Cesàro sum of the series is S if $S=\underset{n\to \infty }{\text{lim}}\frac{1}{n}{\displaystyle {\sum }_1^n{s}_k}$. If a series is convergent to S, then its Cesàro sum is also S, but some divergent series have Cesàro sums; for example, 1−1 + 1−1 + … has a Cesàro sum of ½. The Abel sum generalizes the Cesàro sum still further.