![Searching for the Pattern](http://s1.studyres.com/store/data/012936107_1-cc987add4bee2241cd0868dd2af5b9e6-300x300.png)
Searching for the Pattern
... This pattern consists of four shapes that repeat in the same order. The repeating pattern is: ...
... This pattern consists of four shapes that repeat in the same order. The repeating pattern is: ...
6.4 Recursion Formulas
... Such formulas are known as explicit formulas. They can be used to calculate any term in a sequence without knowing the previous term. For example, the tenth term in the sequence determined by the formula tn = 2n + 3 is 2(10) + 3, or 23. It is sometimes more convenient to calculate a term in a sequen ...
... Such formulas are known as explicit formulas. They can be used to calculate any term in a sequence without knowing the previous term. For example, the tenth term in the sequence determined by the formula tn = 2n + 3 is 2(10) + 3, or 23. It is sometimes more convenient to calculate a term in a sequen ...
7 Sequences of real numbers
... The next question is whether boundedness and an additional property of a sequence can guarantee convergence. It turns out that such an property is monotonicity defined in the following definition. Definition 7.3.3. A sequence {sn }+∞ n=1 of real numbers is said to be non-decreasing if sn ≤ sn+1 for ...
... The next question is whether boundedness and an additional property of a sequence can guarantee convergence. It turns out that such an property is monotonicity defined in the following definition. Definition 7.3.3. A sequence {sn }+∞ n=1 of real numbers is said to be non-decreasing if sn ≤ sn+1 for ...
Sequences: Definition: A sequence is a function whose domain is
... Definition: A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers. We usually use the symbol an to represent a sequence, where n is a natural number and an is the value of the function on n. Intuitively, a sequence is just an ordered list of (possibly ...
... Definition: A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers. We usually use the symbol an to represent a sequence, where n is a natural number and an is the value of the function on n. Intuitively, a sequence is just an ordered list of (possibly ...
Sequence
In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them into computer memory; infinite sequences are also called streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.