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In mathematics, the nth-term test for divergence [1] is a simple test for the divergence of an infinite series: If ...
A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3.
This is also known as the nth-term test, test for divergence, or the divergence test. Ratio test. This is also known as d'Alembert's criterion.
The n th term describes the length of the n th run A000002: Euler's totient function ... The n th Ramanujan prime is the least integer R n for which ...
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
Beginning of the Fibonacci sequence on a building in Gothenburg. In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.. An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms.
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
One such notation is to write down a general formula for computing the nth term as a function of n, enclose it in parentheses, and include a subscript indicating the set of values that n can take. For example, in this notation the sequence of even numbers could be written as ( 2 n ) n ∈ N {\textstyle (2n)_{n\in \mathbb {N} }} .