(Pah! Some noders just don't pick up their nodeshells after the party. I guess *somebody* has to do it...)

We want to exhibit a bounded sequence with no Cesaro limit. Consider the sequence `100111100000000...`, i.e. a one, then 2 zeros, then 4 ones, then 8 zeros etc.

Now for odd *n*, the sum of the first 2^{n} elements contains at least 2^{n-1} + 2^{n-3} ones, namely from the last block and the block two steps earlier. So the average value of the first 2^{n} elements is ≥ (2^{n-1} + 2^{n-3})/2^{n} = 5/8. Similarly, for even *n* the average is ≤ 3/8. This shows that the average value of the sequence does not converge to a limit.