High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! 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. The summation by parts formula is sometimes called Abel's lemma or Abel transformation. Summation is the operation of combining a sequence of numbers using addition; the result is their sum or total. An interim or present total of a summation process is termed the running total. The numbers to be summed may be integers, rational numbers, real numbers, or complex numbers, and other types of values than numbers can be summed as well: vectors, matrices, polynomials, and in general elements of any additive group (or even monoid). For finite sequences of such elements, summation always produces a well-defined sum (possibly by virtue of the convention for empty sums).

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