Suppose that x0 = 1, y0 = 0, xn = xn-1 + 2yn-1, and yn = xn-1
Question:
xn = xn-1 + 2yn-1, and yn = xn-1 + yn-1
for n ∊ N. Prove that x2n - 2y2n = ± 1 for n ∊ N and
xn/yn → √2 as n → ∞
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 53% (15 reviews)
Since x 0 1 and y 0 0 Notice that x 1 1 y 1 If y n1 n 1 and x ...View the full answer
Answered By
Mugdha Sisodiya
My self Mugdha Sisodiya from Chhattisgarh India. I have completed my Bachelors degree in 2015 and My Master in Commerce degree in 2016. I am having expertise in Management, Cost and Finance Accounts. Further I have completed my Chartered Accountant and working as a Professional.
Since 2012 I am providing home tutions.
3.30+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Numerical Analysis questions
-
Suppose that x0 (-1, 0) and xn = xn-1 + 1 - 1 for n N. Prove that xn 0 as n . What happens when x0 [- 1, 0]?
-
Suppose that x 0 = 2\/3, y 0 = 3, and y n = x n y n1 for n e N. a) Prove that x n x and y n y, as n , for some x, y R. b) Prove that x = y and 3.14155 < x < 3.14161. (The actual value of x is .)...
-
Suppose that an object can be at any one of n+1 equally spaced points x 0 , x 1 . . . x n . When an object is at location x i , it is equally likely to move to either x i1 or x i+1 and cannot...
-
An analysis of spending by a sample of credit card bank cardholders shows that spending by cardholders in January (Jan) is related to their spending in December ( Dec): The assumptions and conditions...
-
Bonds issued by the Coleman Manufacturing Company have a par value of $1,000, which of course is also the amount of principal to be paid at maturity. The bonds are currently selling for $690. They...
-
You carry out the following reaction by introducing N 2 O 4 into an evacuated flask and observing the concentration change of the product over time. N 2 O 4 (g) 2NO 2 (g) Which one of the curves...
-
Fill in the Blank. Laminated structures have ____________ damping.
-
Variable costing and absorption costing, the All-Fixed Company (R. Marple, adapted) It is the end of 2011. The All-Fixed Company began operations in January 2010. The company is so named because it...
-
Calculate Ending Inventory using Weighted average (WA) method Syd Gee Ltd Opening Trial Balance 1 June 2021 BANK STATEMENT As at 30 June 2021 DATE PARTICULARS DEBIT CREDIT BALANCE Account Debit...
-
Ryan Ross (111-11-1112), Oscar Omega (222-22-2222), Clark Carey (333-33-3333), and Kim Kardigan (444-44-4444) are equal active members in ROCK the Ages LLC. ROCK serves as agent and manager for...
-
Let 0 < y 1 < x 1 and set a) Prove that 0 < y n < x n for all n e N. b) Prove that y n is increasing and bounded above, and that x n is decreasing and bounded below. c) Prove that 0 < x n+1 y n+1 <...
-
Decide which of the following statements are true and which are false. Prove the true ones and provide a counterexample for the false ones. a) If {xn} is Cauchy and {yn} is bounded, then {xnyn} is...
-
Assume that the energy transferred in the collision between the shell and the armor plate in exercise 12 affects only the shaded area of the armor plate beneath contact with the flat tip of the shell...
-
Let Z (Z,..., Zp) form a random vector where each variable has a N(0, 1) dis- tribution. Let be a positive definite symmetric square matrix and = TT be the Cholesky decomposition of where T is an...
-
(a) The spliced connection shown in the figure below, is under the effect of an axial tension load (N* = 20 kN) originating from transient wind load actions only and acting along the grains of the...
-
The table provides the aggregate plan of It is known that the firm uses a chase plan. The firm's labor cost is $14/un hiring cost is $350 per unit of increase, and unit firing cost is $500 per unit...
-
Sheffield Book Warehouse Ltd. distributes hardcover books to retail stores. At the end of May, Sheffield's inventory consists of 230 books purchased at $17 each. Sheffield uses a perpetual inventory...
-
Dozier Company produced and sold 1,000 units during its first month of operations. It reported the following costs and expenses for the month: Direct Baterials Direct labor Variable manufacturing...
-
Factor the given expressions completely. x 6 y 3 + x 3 y 6
-
Suppose the index goes to 18 percent in year 5. What is the effective cost of the unrestricted ARM?
-
If A, B, and C are mutually exclusive events, is it possible for P (A) = 0.3, P (B) = 0.4, and P (C) = 0.5? Why or why not?
-
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: Shock resistance High Low Scratch high 70 9...
-
The analysis of shafts for a compressor is summarized by conformance to specifications. Roundness conforms Yes No Surface finish yes 345 5 Conforms no 12 8 (a) If a shaft is selected at random, what...
-
Cash Supplies Land Building Total assets TYPHOON, INCORPORATED Balance Sheet December 31, 2024 Assets Liabilities $ 1,100 Accounts payable $ 3,400 Stockholders' Equity 5,400 Common stock 15,400...
-
DeSoto Tools Incorporated is planning to expand production. The expansion will cost $2,600,000, which can be financed either by bonds at an interest rate of 7 percent or by selling 52,000 shares of...
-
Waterway Inc. uses LIFO inventory costing. At January 1, 2025, inventory was $216,014 at both cost and market value. At December 31, 2025, the inventory was $283,252 at cost and $262,660 at market...
Study smarter with the SolutionInn App