Solution-Definition of a cauchy sequence

Definition of a cauchy sequence

Assignment Help Mathematics

Reference no: EM131098702

Question:

Definition of a Cauchy Sequence:

A sequence (a_n) is called a Cauchy sequence if, for every ε > 0, there exists an N ∈ natural number such that whenever m,n ≥ N it follows that |a_n - a_m| < ε.

Sn = (-1)ⁿ/n. For all n in natural number

Prove that the given sequence: S_n is a Cauchy sequence by using DEFINITION.

Reference no: EM131098702

Questions Cloud

What was the duration of loan : Jerry borrowed $10,657.50 from his bank to build an attached garage and work space on his house. Jerry's simple interest loan had a rate of 13% and required him to pay $12,250 under the agreed terms. What was the duration of his loan?

Non inverted sections of nonlinear optical material : Quasi-phase-matching. Generalize the discussion of the text leading from Eq. (2.4.1) to Eq. (2.4.6) by allowing the lengths of the inverted an non inverted sections of nonlinear optical material to be different.

Long standing question of interest to economists : A long standing question of interest to economists who study education is how outcomes vary for students who attend private schools as compared to public schools. The authors of this article have data on a standardized test taken when each student wa..

What are the forces on the two supports at the end of bridge : what are the forces on the two supports at the end of the bridge?

Definition of a cauchy sequence : Definition of a Cauchy Sequence: A sequence (an) is called a Cauchy sequence if, for every ε > 0, there exists an N ∈ natural number such that whenever m,n ≥ N it follows that |an - am|

Generalize the result of the previous problem : Mode structure of an optical cavity. Generalize the result of the previous problem to the situation in which the cavity length is L but the material medium has length Lc

Determining the example of a function : Use the library or Internet to find another example of a function. Explain how it works with a three sets of inputs for your example. What is the output of your data? What is the practical use of your function?

What legal arguments were made by the losing party : What are all of the elements of the main legal rule that this case illustrates? For instance, if the case is about undue influence, list ALL of the elements that the court in this case said had to be proven by the plaintiff.

Does machine have any future worth if the interest rate : An engineer is considering the purchase of a copy machine for his/her consulting office. The copy machine will cost $2,000 and have a resale value of $400 at the end of its 5-year life. Having the machine in the office will reduce copy costs by $1,00..

User Account

All Pages

Definition of a cauchy sequence

Reference no: EM131098702

Reference no: EM131098702

Questions Cloud

Reviews

Write a Review

Mathematics Questions & Answers

Questions on ferris wheel

Logistic map

Finding the probability of cards

Systems of ode

Derive the boolean expression

System of equations

Linear programming problem

Find the natural domain

Introduction to numerical methods

Chart of the topological manifold

Mathematics in computing

Complex problems

Assured A++ Grade

Academics

Major Subjects

Majors

Get In Touch

TERMS & POLICIES

HELP & SUPPORT