Show that the sequence defined by an1 = 2, an+1 = 1/3 an satisfies 0 <

Question:

Show that the sequence defined by an1 = 2, an+1 = 1/3 – an satisfies 0 < an < 2and is decreasing. Deduce that the sequence is convergent and find its limit.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0538497909

7th edition

Authors: James Stewart

See More Books

Question Posted: Jul 10, 2010 01:18 AM

See More Questions

Show that the sequence defined by a1 = 1, an+1 = 3 1/an is increasing and an < 3 for all a. Deduce that {an} is convergent and find its limit.
Show that the sequence defined by a1 = 1, an+1 = 3 - 1/an Is increasing and an < 3 for all n. Deduce that {an} is convergent and find its limit.
Find the first 40 terms of the sequence defined by and a1 = 11. Do the same if a1 = 25. Make a conjecture about this type of sequence. if a, is an even number Sta, 3a, +1 if a, is an odd number
Pritchett Company reported the following year-end data: Cash $ 25,000 8,000 Short-term investments Accounts receivable (current) Inventory 19,500 27,500 Prepaid (current) assets 11,000 Total current...
Find the z-score such that the area under the standard normal curve to its right is 0.25. Find the indicated z-score. Be sure to draw a standard normal curve that depicts the solution.
Explain the overload of accounting standards. How is the FASB attempting to overcome this issue?
The assembly consists of two 12-mm-diameter A992 steel rods AB and CD, a 20-mm-diameter 6061-T6 aluminum rod EF, and a rigid bar AEC. If P = 20 kN, determine the displacement of end F of rod EF. 600...
The following information pertains to the payroll of Texera Tile Company on June 3: a. The total wages earned by employees are $17,210. b. The state unemployment insurance contribution rate is 3.5%....
Suppose you observed that one-year T-bills are trading with a yield to maturity (YTM) of 4.75%. The yield spread between AAA and BB rated corporate bonds is 130 basis points. The maturity yield...
Read the case study "Southwest Airlines," found in Part 2 of your textbook. Review the "Guide to Case Analysis" found on pp. CA1 - CA11 of your textbook. (This guide follows the last case in the...
A sequence {an} is given by a1 = 2, an+1= 2 + an. (a) By induction or otherwise, show that {an} is increasing and bounded above by 3. Apply Theorem 11 to show that lim n an exists (b) Find lim n an.
(a) Fibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair which becomes productive at age 2 months. If we start with one newborn...
The roller-coaster track shown is contained in a vertical plane. The portion of track between A and B is straight and horizontal, while the portions to the left of A and to the right of B have radii...
Consider the following information and determine how Smith & Company's audit report should be dated. Explain your answer: ABC Bank's balance sheet is dated December 31, 2019. On January 12, ABC's...
Iron-56, Fe, has a binding energy per nucleon of 8.79 MeV. (1 MeV = 1.60 10 J). Determine the amount of energy, in J, needed to 'decompose' 1 mol of iron-56 nuclei into the individual nucleons.
Two ice skaters of identical mass approach on parallel paths 1.60 [m] apart. Both are moving at 5.40 [m/s]. As they pass they join hands, maintaining their 1.60 [m] separation, and begin rotating...
what is your understanding of the 4th amendment? can police officer ask the driver and the occupants of a vehicle to exit of the car? what is your understanding of consent search? references:...
A rock on the ground is moved either vertically or horizontally. First it is accelerated horizontally from rest to a speed of 10 m/s. After it is stop to rest it is lifted vertically very slowly...
The following financial statement for the First National Bank is for the current year. After you review the data, calculate the duration gap for the bank. First National Bank Duration Assets (in...
A Firm intends to invest some capital for a period of 15 years; the Firm's Management considers three Options, each consisting of purchasing a machinery of a specific brand, different for each...
Is expansionary fiscal policy more attractive to politicians who believe in larger government or to politicians who believe in smaller government? Explain your answer.
Sketch the region bounded by the curves. y = 3x, y = x 2
Sketch the region bounded by the curves. y = 4 x 2 , x 2y = 2
Find an equation of the parabola with vertex (1, 1) that passes through the points (1, 3) and (3, 3).
What is the role of education in promoting social mobility and reducing inequality, and how can educational systems be reformed to better serve diverse populations while preparing individuals for the...
A European call option and put option on a non-dividend paying stock both have a strike price of $51 and an expiration date in 6 months. The put sells for $2.50 and the call sells for $2. The...
Larkspur Company sells discounted shoes to the fashion-oriented consumer. The following schedule relates to the company's inventory for the month of March: Cost Sales March 1 Beginning inventory...

Show that the sequence defined by an1 = 2, an+1 = 1/3 an satisfies 0 <

Question:

Step by Step Answer:

We use induction Let P be the statement that 0 an1 an 2 Clearly P is true ...View the full answer

Calculus Early Transcendentals

Students also viewed these Calculus questions