b) Show that limn-n = x ≥ 0 if there is NE N, such that, for k2 N, k ≥ 0.Please follow stepsbelow. Use the argument by contradiction:• Suppose that there is NE N, such that, for k≥ N, ak 20 andn = x < 0.lim818

We need to show that if there is such that, for , .We need to show this result by argument of…

Answered: contradiction: Show that limnoo n = x ≥…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

b) Show that limn-
n = x ≥ 0 if there is NE N, such that, for k2 N, k ≥ 0.
Please follow steps
below. Use the argument by contradiction:
• Suppose that there is NE N, such that, for k≥ N, ak 20 and
n = x < 0.
lim
818

Expert Solution

Step 1: Introduction

We need to show that $limit as n rightwards arrow infinity of x subscript n equals x greater or equal than 0$ if there is $N element of straight natural numbers$ such that, for $k greater or equal than N$ , $x subscript k greater or equal than 0$ .

We need to show this result by argument of contradiction.

We know that $limit as n rightwards arrow infinity of x subscript n equals x$ , if for all $epsilon greater than 0$ , there exists $N element of straight natural numbers$ such that $open vertical bar x subscript n minus x close vertical bar less than epsilon$ for all $n greater or equal than N$ .