HW #5 - WSU EECS
... Don’t be intimidated by this formula. It simply states that the “next” value in the sequence relative to the nth term is the sum of the nth term and the n − 1th term. We can “seed” the sequence by starting with the first two terms to obtain the third: x2 = x1 + x0 ...
... Don’t be intimidated by this formula. It simply states that the “next” value in the sequence relative to the nth term is the sum of the nth term and the n − 1th term. We can “seed” the sequence by starting with the first two terms to obtain the third: x2 = x1 + x0 ...
SEQUENCES Learning Objectives
... the sequence by using a rule to work out any number by using it’s position in the sequence. This method is known as the position to term method. ...
... the sequence by using a rule to work out any number by using it’s position in the sequence. This method is known as the position to term method. ...
INTRODUCTION TO THE CONVERGENCE OF SEQUENCES
... We know this converges to 1 and can verify this using the same logic used in the proof under the definition of convergence showing that n1 converges to zero. Therefore, as n becomes very large, xn approaches 1, but is never equal to 1. By the above theorem, we know that this sequence is bounded beca ...
... We know this converges to 1 and can verify this using the same logic used in the proof under the definition of convergence showing that n1 converges to zero. Therefore, as n becomes very large, xn approaches 1, but is never equal to 1. By the above theorem, we know that this sequence is bounded beca ...
Arithmetic and Geometric Sequences
... there are infinitely many primes p such that the principal period in the decimal expansion of 1/p has exactly p − 1 digits. 13. A positive integern is called a perfect number, if it is equal to the sum of all its positive divisors smaller than n. For example, 6 = 1 + 2 + 3, 28 = 1 + 2 + 4 + 7 + 14, ...
... there are infinitely many primes p such that the principal period in the decimal expansion of 1/p has exactly p − 1 digits. 13. A positive integern is called a perfect number, if it is equal to the sum of all its positive divisors smaller than n. For example, 6 = 1 + 2 + 3, 28 = 1 + 2 + 4 + 7 + 14, ...
a n+1
... have 2 limits, L1 and L2. Than for a given ∃N 1 ∈N:∀n∈N:n>N 1 :|L1 −xn|<ϵ ∃N 2 ∈N:∀n∈N:n>N 2 :| L2 −xn|<ϵ if N=max{N 1 ,N 2 }, xn would be arbitrary close to L1 and arbitrary close to L2 at the same, it is impossible-this is the contradiction (Unless L1 =L2) ...
... have 2 limits, L1 and L2. Than for a given ∃N 1 ∈N:∀n∈N:n>N 1 :|L1 −xn|<ϵ ∃N 2 ∈N:∀n∈N:n>N 2 :| L2 −xn|<ϵ if N=max{N 1 ,N 2 }, xn would be arbitrary close to L1 and arbitrary close to L2 at the same, it is impossible-this is the contradiction (Unless L1 =L2) ...
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.