CALC 1501 LECTURE NOTES 4. SEqUEnCEs Definition 4.1. A
... {fn } are 1 and 1, and each consequent number is the sum of the previous two. Inductively this can be defined as follows. f1 = f2 = 1, fn = fn−1 + fn−2 , for n > 2. The first several terms of the Fibonacci sequence can be easily computed to be ...
... {fn } are 1 and 1, and each consequent number is the sum of the previous two. Inductively this can be defined as follows. f1 = f2 = 1, fn = fn−1 + fn−2 , for n > 2. The first several terms of the Fibonacci sequence can be easily computed to be ...
Sequences I
... Let C > 0. Since (an ) → ∞ and C/2 > 0 there exists a natural number N1 such that an > C/2 whenever n > N1 . Also, since (bn ) → ∞ and C/2 > 0 there exists a natural number N2 such that bn > C/2 whenever n > N2 . Now let N = max{N1 , N2 }. Suppose n > N . Then n > N1 and n > N2 so that an > C/2 and ...
... Let C > 0. Since (an ) → ∞ and C/2 > 0 there exists a natural number N1 such that an > C/2 whenever n > N1 . Also, since (bn ) → ∞ and C/2 > 0 there exists a natural number N2 such that bn > C/2 whenever n > N2 . Now let N = max{N1 , N2 }. Suppose n > N . Then n > N1 and n > N2 so that an > C/2 and ...
C# Fundamentals - Intermediate Exam
... A spiral of increasing numbers in the matrix is any sequence of at least two or more increasing numbers that starts from a certain cell, continues on the left, up, right or down, and then runs in the form of a spiral around the starting cell in either clockwise or counterclockwise direction. The inp ...
... A spiral of increasing numbers in the matrix is any sequence of at least two or more increasing numbers that starts from a certain cell, continues on the left, up, right or down, and then runs in the form of a spiral around the starting cell in either clockwise or counterclockwise direction. The inp ...
Econ 204 Supplement to Section 2.3 Lim Sup and Lim Inf Definition
... Definition 2 [Definition 3.7 in de La Fuente] If {xn } is a sequence of real numbers, we say that {xn } tends to infinity (written xn → ∞ or limn→∞ xn = ∞) if ∀K ∈ R ∃N(K) s.t. n > N(K) ⇒ xn > K Similarly, we say limn→∞ xn = −∞ if ∀K ∈ R ∃N(K) s.t. n > N(K) ⇒ xn < K Definition 3 Consider a sequence ...
... Definition 2 [Definition 3.7 in de La Fuente] If {xn } is a sequence of real numbers, we say that {xn } tends to infinity (written xn → ∞ or limn→∞ xn = ∞) if ∀K ∈ R ∃N(K) s.t. n > N(K) ⇒ xn > K Similarly, we say limn→∞ xn = −∞ if ∀K ∈ R ∃N(K) s.t. n > N(K) ⇒ xn < K Definition 3 Consider a sequence ...
12.3 Geometric Sequences Series
... Precalculus 12.3 Geometric Sequences; Geometric Series Objective: able to determine if a sequence is geometric; find a formula for a geometric sequence; find the sum of a geometric sequence (a geometric series). ...
... Precalculus 12.3 Geometric Sequences; Geometric Series Objective: able to determine if a sequence is geometric; find a formula for a geometric sequence; find the sum of a geometric sequence (a geometric series). ...
Sequences and Series
... An arithmetic sequence is one where a constant value is added to each term to get the next term. example: {5, 7, 9, 11, …} A geometric sequence is one where a constant value is multiplied by each term to get the next term. example: {5, 10, 20, 40, …} EXAMPLE: Determine whether each of the following ...
... An arithmetic sequence is one where a constant value is added to each term to get the next term. example: {5, 7, 9, 11, …} A geometric sequence is one where a constant value is multiplied by each term to get the next term. example: {5, 10, 20, 40, …} EXAMPLE: Determine whether each of the following ...
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.