Calculate the Cesaro sums of the series
1-1+0+1-1+0+1-1+0+1-1+0+···
1-1+0+0+1-1+0+0+1-1+0+0+···
Both series are generated from the series 1 - 1 + 1 - 1 + · · · by inserting 0s into this sum. As you will see, by doing so the Cesaro sum changes. On the other hand, given a convergent (in the standard way) series, will it's sum change if you insert 0s into it? Explain.