# Cesàro Summation

Cesàro Summation

The Cesàro sum of an infinite series is given by , provided that this limit exists. If a convergent series has sum , then it is Cesàro summable and has Cesàro sum . A divergent series may still have a well-defined Cesàro sum. This Demonstration considers the series sin(k), which is classically divergent but has the Cesàro sum cot.

∞

∑

k=0

f

k

lim

m∞

1

m+1

m

∑

n=0

n

∑

k=0

f

k

S

S

∞

∑

k=0

1

2

1

2