Wolfram Demonstrations Project

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.

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

Contributed by: George Beck

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Cesàro Sums of Some Unit Sequences