rekursjonsformel

A recursion formula, also known as a recursive formula or recurrence relation, is a mathematical expression that defines a sequence in terms of its preceding terms. It is a fundamental concept in mathematics and computer science, particularly in the study of algorithms and data structures. Recursion formulas are often used to describe sequences that are defined by a simple rule applied repeatedly.

In its simplest form, a recursion formula can be written as:

a_n = f(a_{n-1}, a_{n-2}, ..., a_{n-k})

where a_n represents the nth term of the sequence, and f is a function that depends on the previous k terms of the sequence. The initial terms of the sequence, a_1, a_2, ..., a_k, are typically given and are known as the base cases.

Recursion formulas are particularly useful in situations where it is difficult or impossible to find a closed-form expression for the sequence. They are also commonly used in the analysis of recursive algorithms, where the time or space complexity of the algorithm can be described by a recursion formula.

One of the most well-known examples of a recursion formula is the Fibonacci sequence, which is defined by the formula:

F_n = F_{n-1} + F_{n-2}

with base cases F_1 = 1 and F_2 = 1. This formula defines the sequence of Fibonacci numbers, which have many interesting properties and applications in mathematics and computer science.

In summary, a recursion formula is a mathematical expression that defines a sequence in terms of its preceding terms. It is a powerful tool for describing sequences that are defined by a simple rule applied repeatedly, and it has many applications in mathematics and computer science.