Gesamtsumme

Gesamtsumme is a German term that denotes the total amount obtained by adding together all components of a set, list, or sequence. It is used in mathematics, statistics, accounting, and everyday language to express the final aggregate value.

In mathematics, the Gesamtsumme of a finite collection a1, a2, ..., an is S = a1 + a2 + ... + an. For a sequence, the running total up to a given index k is called the laufende Summe; the final value for a finite list is the Gesamtsumme. For an infinite series, the Gesamtsumme exists if the series converges to a finite limit; otherwise the series diverges. The term is often used interchangeably with Summe in everyday language, though Gesamtsumme emphasizes the complete total.

In practical contexts, the Gesamtsumme represents the total of several items or categories, such as total revenue, total expenses, or the total score across components. It is commonly seen on receipts or invoices as the grand total, often presented alongside subtotals.

Etymology and related terms: gesamt means overall or total, and Summe means sum. Related concepts include Summe, laufende Summe (running total), and kumulative Summe (cumulative sum).