Reihen
Reihen is a German term with several related uses. In mathematics, a Reihe denotes a series, the sum of the terms of a sequence. The corresponding object describing the original sequence is called a Folge. An infinite series is written as sum from n = 1 to infinity of a_n, with partial sums S_N = a_1 + a_2 + ... + a_N. The series is convergent if S_N tends to a finite limit as N grows; otherwise it diverges. Convergence is studied using tests such as the geometric test (a geometric series with ratio r converges if |r| < 1), the ratio test, the comparison test, and the root test. Convergence can be absolute or conditional, and many series have important closed forms, for example the geometric series sum_{n=0}^\infty r^n = 1/(1-r) for |r| < 1.
In everyday language, Reihe also means a row or line of objects arranged side by side, as
The plural form Reihen can indicate multiple series or rows. In German mathematical terminology, it is important
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