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2. Summation by parts - Wikipedia

   en.wikipedia.org/wiki/Summation_by_parts

   In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.

3. Harmonic series (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Harmonic_series_(mathematics)

   It is a divergent series: as more terms of the series are included in partial sums of the series, the values of these partial sums grow arbitrarily large, beyond any finite limit. Because it is a divergent series, it should be interpreted as a formal sum, an abstract mathematical expression combining the unit fractions, rather than as something ...

4. Summation of Grandi's series - Wikipedia

   en.wikipedia.org/wiki/Summation_of_Grandi's_series

   The basic idea is similar to Leibniz's probabilistic approach: essentially, the Cesàro sum of a series is the average of all of its partial sums. Formally one computes, for each n, the average σ n of the first n partial sums, and takes the limit of these Cesàro means as n goes to infinity. For Grandi's series, the sequence of arithmetic means is

5. Cesàro summation - Wikipedia

   en.wikipedia.org/wiki/Cesàro_summation

   In mathematical analysis, Cesàro summation (also known as the Cesàro mean [1] [2] or Cesàro limit [3]) assigns values to some infinite sums that are not necessarily convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series.

6. Divergent series - Wikipedia

   en.wikipedia.org/wiki/Divergent_series

   In specialized mathematical contexts, values can be objectively assigned to certain series whose sequences of partial sums diverge, in order to make meaning of the divergence of the series. A summability method or summation method is a partial function from the set of series to values. For example, Cesàro summation assigns Grandi's divergent ...

7. Partial sums - Wikipedia

   en.wikipedia.org/?title=Partial_sums&redirect=no

   This page was last edited on 19 December 2004, at 20:24 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.