Question: Prove that if the sequence { an } is convergent and lim an = L, then the sequence {an } is also convergent and lim

Prove that if the sequence { an } is convergent and

lim an = L, then the sequence {an } is also convergent

Prove that if the sequence { an } is convergent and lim an = L, then the sequence {an } is also convergent and lim an 2 = 12. n- too

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:

Let r 1 and r 2 be the roots of (x) = ax 2 2x + 20. Observe that approaches the linear function L(x) = 2x + 20 as a 0. Because r = 10 is the unique root of L, we might expect one of the roots of ...

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:

# 7 (chapter 5)(40 points, Due on Friday November 11) Question 1. [3 points each] Use the definition of Limit of functions to prove that x2 2 . 5 5 2 lim x 3 x 1 1 (B) x 1 (A) lim x 0 if x 2 2x (C)...

Q:

Consider the sequence of functions f n : [ 0 , 1 ] R defined as f n ( x ) = x n which converges pointwise to f : [ 0 , 1 ] R . a) Use one of the results of Theorem 3.2.2. Let {f,} be a sequence of...

Q:

Consider the sequence of functions f n : R R defined as Theorem 3.2.2. Let {f,} be a sequence of functions with common domain D, and let c be a point of I. Suppose that for all n E Z+ we have lim...

Q:

I would like to know how to prove these theorems, for part 1,3, and 4. Thanks! Theorem : If the sequence fang and Ebn are convergent to L and m respectively, (ire limanz L and timbr= M. ) Then? The...

Q:

Series - Ratio and Root Tests: Problem 13 (1 point) Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive. i\": ( n + 15 )" ":1...

Q:

1. Which of the following is not true about sequence an = n A. The sequence converges to 0. B. lim a = L, for some finite L. t=1 C. The series (-1)"an converges. D. The series a converges. 2. Which...

Q:

# 6 (Chapter 4)(20 points, Due on Wednesday, October 26) Question 1. [3 points each] Use the Monotone Convergence Theorem to prove that each of the following sequences is convergent and then find the...

Q:

4. Determine if the series converges absolutely, converges conditionally, or diverges. (Show all of your work!) (a) 22:2 2:1?\" 00 1 \"'1 (b) 271:1 ( % (71)\"(n'i'lllt4 (Cl 220:1 "2 Ratio Test...

Q:

Why does your body get more rest when you're lying down than when you're sitting? Is blood pressure in your legs greater?

Q:

In general, how is the cost of internally generated intangibles accounted for?

Q:

(i) Find a formula for the sum S of any three consecutive even numbers. (ii) Hence, calculate the value of S when the smallest even number is 14.

Q:

Evaluating Credit Policy Air Spares is a wholesaler that stocks engine components and test equipment for the commercial aircraft industry. A new customer has placed an order for eight high-bypass...

Q:

The company started business at the beginning of Year 1. Inventory purchases and sales during the first four years of the company's business are as follows: Compute the company's ending inventory as...

Q:

At the beginning of September, Selena Cantu started Cantu Wealth Management Consulting, a firm that offers financial planning and advice about investing and managing money. On September 30, the...

Q:

Presented below is information for Furlow Company for the month of March 2019. Cost of goods sold......................$212,000.................Rent expense...............$ 32,000...

Q:

Milan Co., a womens clothing store, purchased $120,000 of merchandise from a supplier on account, terms FOB destination, 2/10, n/30. Milan Co. returned $16,000 of the merchandise, receiving a credit...

Q:

Tori and some other childeen experimented with balls to see which ones rolled. First using a piece of cardboard to use as a ramp, they angled it on a block to the floor to test the balls. Then Tori...

Q:

identify the causes of labour, material, overhead and sales margin variances; LO1

Q:

construct a departmental performance report; LO1

Q:

Calculate the materials variances from the following data: (i) Material A: Standard price per tonne 10 Standard usage per unit 30 tonnes Actual price per tonne 9 Actual usage per unit 35 tonnes (ii)...