Explanation Given : A convergent sequence { a n } of integers with limit L Calculation : Step 1: Suppose { a n } converges to L, let ε = 1 2 . Then there exists a number M, such that | a n − L | < 1 2 for all n ≥ M Step 2: So, for all n ≥ M , L − 1 2 < a n < L + 1 2 ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

See similar textbooks

Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

Videos

Question

Chapter 11.1, Problem 78E

To determine

With help of the limit definition, the mathematical proof of the statement stating that if ${a_{n}}$ is a convergent sequence of integers with limit L, then there exists a number M such that $a_{n} = L$ for all $n \geq M$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.1, Problem 77E

Chapter 11.1, Problem 79E

Students have asked these similar questions

i need help please . and please dont use chat gpt i am trying to learn and see the mistake i did when solving mine

The radius of a sphere decreases at a rate of 3 m/s. Find the rate at which the surface area decreases when the radius is 8 m. Answer exactly or round to 2 decimal places. The surface area decreases at a rate of m²/s

Chapter 11 Solutions

Calculus - Standalone book

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

With help of the limit definition, the mathematical proof of the statement stating that if { a n } is a convergent sequence of integers with limit L, then there exists a number M such that a n = L for all n ≥ M .

Solution Summary: The author explains the mathematical proof of the statement stating that if a n

Concept explainers

Videos

With help of the limit definition, the mathematical proof of the statement stating that if ${a_{n}}$ is a convergent sequence of integers with limit L, then there exists a number M such that $a_{n} = L$ for all $n \geq M$ .

Want to see the full answer?

Chapter 11 Solutions

With help of the limit definition, the mathematical proof of the statement stating that if { a n } is a convergent sequence of integers with limit L, then there exists a number M such that a n = L for all n ≥ M .

Solution Summary: The author explains the mathematical proof of the statement stating that if a n

Concept explainers

Videos

With help of the limit definition, the mathematical proof of the statement stating that if {an} is a convergent sequence of integers with limit L, then there exists a number M such that an=L for all n≥M.

Want to see the full answer?

Chapter 11 Solutions

With help of the limit definition, the mathematical proof of the statement stating that if ${a_{n}}$ is a convergent sequence of integers with limit L, then there exists a number M such that $a_{n} = L$ for all $n \geq M$ .