Prove that if an is a conditionally convergent series and r is any real number, then there

Question:

Prove that if Σ an is a conditionally convergent series and r is any real number, then there is a rearrangement of Σ an whose sum is

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 978-0131429246

9th edition

Authors: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon

See More Books

Question Posted: Jul 10, 2010 01:50 AM

See More Questions

Explain why a conditionally convergent series can be rearranged to converge to any given number?
Prove that if (an is convergent series of positive terms then (In (1 + an) converges?
Prove that if E R is connected, then Eo is also connected. Show that this is false if R is replaced by R2.
In your opinion, which companies (healthcare or non-healthcare related) provide superior customer service? Which companies provide average or mediocre customer service? Name the factors most...
Historically, the probability that a passenger will miss a flight is 0.0995. Source: Passenger-Based Predictive Modeling of Airline No-show Rates by Richard D. Lawrence, Se June Hong, and Jacques...
Neon Light Company of Kansas City ships lamps and lighting appliances throughout the country. Ms. Neon has determined that through the establishment of local collection centers around the country,...
Cold Appliances Pty Ltd makes refrigerators and is trying to determine the cost of its ending work in process. The accountant has put together the following data for the year ended 30 June 2025. Each...
Adia owns a house and has an elderly third cousin living with her. Adia decides she needs fire insurance on the house and a life insurance policy on her third cousin to cover funeral and other...
These are the pieces you must choose from to summarize and comment on in your essay: "EEOC v. Madison Community Unit School District (No. 12 818 F.2d 577 (7th Cir. 1987))" "Sandor v. Safe Horizon,...
Show that if Y|x is linear in x and var(Y|x) is constant, then var(Y|x) = 2 2 (1 2 ).
Given any series Σ an we define a series Σ an+ whose terms are all the positive terms of Σ an and a series Σ an whose terms are all the negative terms of Σ an. To be...
What is a power series?
Explain how to interpret the test statistic U.
The process of obtaining funds from private parties such as investors, venture capital investors, or other companies interested in investing in a business is known as Question 3Answer a. loan...
The bacteria geobacter metallireducens was discovered to acquire a net electric charge by consuming electrons as its energy source. These bacteria often transfer electrons by forming long chains that...
Choose an example from your personal experience and explain the energy transfers and transformations that are taking place. Do the energy transfers obey the law of conservation of energy? Explain...
The electric field 6.0 cm from a small charged object is (1400 N/C, 20 above horizontal). Part A What is the magnitude of the electric field 6.0 cm in the same direction from the object? Express your...
1. What is the magnitude of the momentum of a 9.2-kg eagle flying with a speed of 89.4 m/s? 2. A constant frictional force of 31 N acts on an 87-kg skier for 23 s on level snow. What is the speed...
Suppose Payton took advantage of Medas benefits. Do you believe this would result in feeling less stressed and improvements in well-being? Why or why not?
we have to compute the letter grades for a course. The data is a collection of student records stored in a file. Each record consists of a name(up to 20 characters), ID (8 characters), the scores of...
Is a country for which imports and exports comprise a large fraction of the GDP more likely to adopt a flexible exchange rate or a fixed (hard peg) exchange rate?
The Shannon index (sometimes called the Shannon-Wiener index or Shannon-Weaver index) is a measure of diversity in an ecosystem. For the case of three species, it is defined as H = p 1 ln p 1 p 2 ln...
Let (a) Show that f (x, y) 0 as (x, y) (0, 0) along any path through (0, 0) of the form y = mx a with 0 < a < 4. (b) Despite part (a), show that f is discontinuous at s0, 0d. (c) Show that f is...
If z = f(x, y), where x = r cos and y = r sin , show that 1 az 1 az dx? dy? ar? + .2 r a0? r r
Explain the concept of hybrid thread models in operating systems. How do they attempt to combine the benefits of user-space and kernel-space threading ?
Describe the characteristics of the six stages of development for intimacy in a romantic relationship using a real or hypothetical example to illustrate the general developmental path.
Consider the following payoff matrix: Player 1 Strategy B Strategy A Strategy A (4,3) (6,2) Player 2 Strategy B (3,5) (2,4) Is the payoff matrix symmetric (Yes or No)?

Prove that if an is a conditionally convergent series and r is any real number, then there

Question:

Step by Step Answer:

Let br be the rearranged series constructed in the hint This series can be c...View the full answer

Calculus

Students also viewed these Calculus questions