| 11. | Whenever a series is Ces�ro summable, it is also Abel summable and has the same sum.
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| 12. | If a series is convergent, then it is Ces�ro summable and its Ces�ro sum is the usual sum.
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| 13. | Hence we say that any sequence a _ n is Ces�ro summable to some " a " if
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| 14. | The above definitions work for signals that are square integrable, or square summable, that is, of finite energy.
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| 15. | Beckman and Quarles also provide a counterexample for Hilbert space, the space of square-summable sequences of real numbers.
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| 16. | For any convergent sequence, the corresponding series is Ces�ro summable and the limit of the sequence coincides with the Ces�ro sum.
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| 17. | The implication is that the Fourier series of any continuous function is Ces�ro summable to the value of the function at every point.
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| 18. | Generally, the terms of a summable series should decrease to zero; even could be expressed as a limit of such series.
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| 19. | On the other hand, taking the Cauchy product of Grandi's series with itself yields a series which is Abel summable but not Ces�ro summable:
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| 20. | On the other hand, taking the Cauchy product of Grandi's series with itself yields a series which is Abel summable but not Ces�ro summable:
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