Explanation Given: number A with the property that a n ≤ A for all n but if c is a number such that c < A , then a m > c for at least one m. Proof: Sequence: A sequence is a function whose domain is a set of non-negative integers and whose range is subset of real numbers. Convergence of a sequence: A sequence is a said to be convergent if it’s increasing and it’s bounded above or decreasing= with bounded below. Refer to the following property; a n ≤ A If c < A , For at least one m, a m > c Consider that; A − ε < a n < A

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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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.

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Chapter 8.1, Problem 55PS

To determine

To show:If ∈>0 is given, there exists a positive integer N so that A−ε<an<A .

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Chapter 8.1, Problem 54PS

Chapter 8.1, Problem 56PS

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Chapter 8 Solutions

Calculus

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