Question: Suppose that limn( nan = 1. Prove that (an diverges?

Suppose that limn→( nan = 1. Prove that (an diverges?

Step by Step Solution

★★★★★

3.44 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If then there is some positive integer N such that a... View full answer

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

Document Format (1 attachment)

Word file Icon

955-M-C-D-E (2526).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Define L : (0, ) R by a) Prove that L is differentiable and strictly increasing on (0, ), with L'(x) = 1/x and L(l) = 0. b) Prove that L(x) as x and L(x) - as x 0+. (You may wish to prove for...

Q:

Prove that if (an diverges, so does (|an|?

Q:

Prove that limn (- l)k/k exists and is finite.

Q:

Math 131A Homework 3 Due: February 3rd, 2017 This assignment is due on February 3rd, 2017 at the beginning of lecture. Provide complete well-written solutions to the following exercises. Please note...

Q:

MATH 401 INTRODUCTION TO ANALYSIS-I, SPRING TERM 2016, PROBLEMS 11 Return by Monday 4th April 1. Prove that if x > 0 and xn is a sequence with limn xn = x, then there is a real number N such that...

Q:

1 For each of the two sequences, determine if it converges. If it does, provide the limit and prove the convergence. If it doesn't, provide a proof that the sequence diverges. a. xn = n ^2/5 /(n^...

Q:

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

Q:

Section 10.4 Reading Assignment: Comparison Tests Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three questions very carefully...

Q:

Let (an) be a sequence of positive numbers such that _,- an converges to some number S. (a) For n 2 1, let by = an + 2an-1 + 3an-2+ ...+ (n -1)a2 + na1 n (n + 1) Prove that En bn diverges. (b) For n...

Q:

(1) Prove that if P(B) = 0 then B and A are independent for any event A. Prove the same if P(B) = 1. (2) Roll two fair die and let X1, X2 be their values. (a) Calculate P(X1 = 6|X1 + X2 = 10). (b)...

Q:

At the end of the year, Kyler Electronic Corporation had the following balances: Work in process $ 43,600 Cash and cash equivalents 540,000 Finished goods 85,700 Raw materials 25,400 Accounts...

Q:

Answer the following questions about this citation: 26 C. F. R. 163-10(a)(2). a. What does the 26 stand for? b. What does the 163 stand for? c. What does the 6T stand for? d. What does the (a) stand...

Q:

Which mechanism do investors use to protect their investment from dilution? Select all that apply. Question 1 5 Answer a . Full ratchet clause b . Partial ratchet or weighted average clause c ....

Q:

Briefly explain whether you agree with the following observation: Technological change refers only to the introduction of new products, so it is not relevant to the operations of most firms.

Q:

Find the equilibrium when h = 1000 and N c = 1000 and r = 1.65. Can you explain why solutions that start below the equilibrium can shoot off to infinity? Population models with thresholds can also...

Q:

The case in Exercise 1. Describe the long-term dynamics in each of the given cases. Find which ones will beat every time, which display 2:1 AV block, and which show some sort of Wenckebach...

Q:

The case in Exercise 2. Describe the long-term dynamics in each of the given cases. Find which ones will beat every time, which display 2:1 AV block, and which show some sort of Wenckebach...

Q:

Your rich uncle just died and left you a nice gift in his will. You will receive $10,000 per year for five years starting next year. Eight years after that finishes, you will receive $5,000 per year...

Q:

what are some creative examples of a spontaneous generation, black holes, and gray holes? I have this information from my book but I'm kind of confused. Spontaneous generation. The APPLY INSURANCE...

Q:

Please help with question. Avoid question already bubbled in. 10) A college student is about to purchase a car when the salesman recommends that he should sign up for a protection plan. Under this...