Summe

Summe is the German noun for the result of adding numbers, i.e., the sum or total. It is used in mathematics and in everyday language to denote the aggregate amount obtained by summing values. The term can refer to the sum of a finite set, the total on a bill, or the overall quantity in a collection. Related words include summieren (to sum), die Summe (singular), die Summen (plural), die Gesamtsumme (the grand total), and die Zwischensumme (the subtotal).

In mathematics, the Summe of a finite sequence a1, a2, ..., an is a1 + a2 + ... + an. For a sequence (a_n), the partial sums S_n = sum_{k=1}^n a_k are used; in series theory, the limit of S_n, when it exists, is called the sum of the series. The standard notation for summation is the sigma symbol Σ, but in prose the operation is described as the Summe.

Etymology-wise, Summe derives from the German word for total, ultimately tracing to Latin summa meaning “the whole” or “the total,” with forms that passed into German through historical development of the language.

Usage notes: In finance and commerce, die Gesamtsumme indicates the final total, while die Zwischensumme refers to a subtotal on an invoice or statement. In programming and statistics, Summe can describe the aggregation of values, sometimes implemented as a summation function. The term is widely understood across German-speaking contexts as the standard label for an additive total.

Example: 2 + 3 = 5; die Summe ist 5.