Question: 3. Let (an) be a sequence such that lim inf(|a, [) = 0. (a) Prove that for any real number r > 0, there exists

3. Let (an) be a sequence such that lim inf(|a, [)

= 0. (a) Prove that for any real number r > 0,

3. Let (an) be a sequence such that lim inf(|a, [) = 0. (a) Prove that for any real number r > 0, there exists infinitely many an's such that lan)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

3 Let (an) be a sequence such that lim inf(|a, ]) = 0. (a) Prove that for any real number > > 0, there exists infinitely many on 's such that Jan)

Q:

3. Let (an) be a sequence such that lim inf(|an)) = 0. (a) Prove that for any real number r > 0, there exists infinitely many an's such that lan|

Q:

Recall that N is the set of positive integers and Q is the set of rational numbers. NOTE: "Limit point\Sequences - Part 2 (Week 4) Infinite Limits Definition. A sequence (sn) is said to diverge to +...

Q:

These are the questions on mathematical analysis Problem la(15 marks) Prove that there exist infinitely many real number v sack that the equation 10 -trip= xy does not have any solution with x yE Q...

Q:

1.(10 points.) Let the set A be defined as follows. That is, A is the set of real numbers between 0 and 1. Invent a way to represent the members of A using only sets. You are also allowed to use...

Q:

(Discrete math for computer science) Hi I need help for solving this problem!! please solve this problem with kind explanation please!! This homework is about representing things in terms of sets,...

Q:

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

Proofs involving Convergent and Divergent sequences Prove the following: (a) lim 0 ([b) lim n1/3 =0 (c) lim 2n-1 3n+2 (d) lim n+6 712-6 .= 0 Determine the limits of the following sequences, and then...

Q:

Let f: A B. If {B1, B2, B3, . . . , Bn} is a partition of B, prove that {f-1(Bt) | l i n, f-l(Bt) } is a partition of A.

Q:

Given the radius of the solid shaft A-B is 40 mm and the shear modulus is 75 GPa, find the maximum shear stress in the shaft. Assume that point B is fixed, whereas point A is a flexible support...

Q:

use the folllwoing information about sunoco stock. HI 9 3 . 7 5 LO 5 0 . 7 5 STOCK SUN DIV 1 . 2 6 YLD % 1 . 1 P / E 5 VOL ( 1 0 0 0 s ) 4 , 8 9 8 CLOSE 6 3 . 7 8 NET CHG + 0 . 9 7 what was the...

Q:

Additional to these instructions: For each answer, which power base would work best? 9. If a person makes each of the following claims, which of the leadership style would fit best that person? Why?...

Q:

2. In what way can we say that method affects the result we get?

Q:

4. In what way will relationships in a system influence what is reported?

Q:

3. Mention three examples where you distorted information that you had taken from your memory and where others made you aware of the fact that you had distorted the information. Did it create a...