Cesàro Sums of Some Unit Sequences

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Consider the series with terms , namely . The series does not converge because its sequence of partial sums, , does not have a limit as . However, this sequence has the limit , which is known as its Cesàro sum.

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Experiment with different sign patterns to see the effect on the averages of the partial sums of the terms.

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Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA


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