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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. Telescoping series - Wikipedia

    en.wikipedia.org/wiki/Telescoping_series

    In mathematics, a telescoping series is a series whose general term is of the form = +, i.e. the difference of two consecutive terms of a sequence ().As a consequence the partial sums of the series only consists of two terms of () after cancellation.

  4. Calculator Applications (UIL) - Wikipedia

    en.wikipedia.org/wiki/Calculator_Applications_(UIL)

    The top three individuals and the top team (determined based on the scores of the top three individuals) will advance to the next round. In addition, within each region, the highest-scoring second place team from all district competitions advances as the "wild card" to regional competition (provided the team has four members), and within the state, the highest-scoring second place team from ...

  5. 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 ...

  6. Series (mathematics) - Wikipedia

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

    Using the symbols , for the partial sums of the original series and , for the partial sums of the series after multiplication by , this definition implies that , =, for all , and therefore also , =,, when the limits exist. Therefore if a series is summable, any nonzero scalar multiple of the series is also summable and vice versa: if a series ...

  7. 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 ...

  8. Kahan summation algorithm - Wikipedia

    en.wikipedia.org/wiki/Kahan_summation_algorithm

    The algorithm performs summation with two accumulators: sum holds the sum, and c accumulates the parts not assimilated into sum, to nudge the low-order part of sum the next time around. Thus the summation proceeds with "guard digits" in c , which is better than not having any, but is not as good as performing the calculations with double the ...

  9. Absolute convergence - Wikipedia

    en.wikipedia.org/wiki/Absolute_convergence

    The same definition can be used for series = whose terms are not numbers but rather elements of an arbitrary abelian topological group.In that case, instead of using the absolute value, the definition requires the group to have a norm, which is a positive real-valued function ‖ ‖: + on an abelian group (written additively, with identity element 0) such that:

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