let x1 1 and xn+1=2 1/xn

PDF	447 HOMEWORK SET 6 1. 3.3 3) Let x1 ? 2 and x n+1 := 1 + ? xn converges. Solution We have xn+1 ? xn = 1. (n+1)2. > 0

PDF	Solutions to Homework 6- MAT319 10 nov. 2008 Exercise 1 (# 4). Let x1 = 1 and xn+1 = ?. 2 + xn. Then lim xn = 2. First we show that xn is increasing by using an induction argument. x2 ...

PDF	Solutions to Homework 7- MAT319 17 nov. 2008 Exercise 1 (#13). Let x1 = 2 and xn+1 =2+1/xn. Then xn is contractive and lim xn =1+.

PDF	Order Statistics 1 Introduction and Notation Notation: Let X1X2

PDF	1. hw 6 (1) Let x1 ? R with x 1 > 1. Define (x n) by xn+1 = 2 ? 1 xn xn+1 = 2 ?. 1 xn for n ? N. Show that the sequence is monotone and bounded. What is its limit? Proof. For n = 1 x2 ? x1

PDF	SAMPLE STATISTICS A random sample of size n from a distribution ements of x = [x1x2

PDF	BASIC STATISTICS 1.1. Random Sample. The random variables X1 DISTRIBUTION OF SAMPLE STATISTICS. 2.1. Theorem 1 on squared deviations and sample variances. Theorem 1. Let x1x2

PDF	Math 3150 Fall 2015 HW2 Solutions (a) Let m be the largest integer such that sm < a and let s = limsn. Let x1 = 1 and xn+1 = 3x2 n for n ? 1. ... n ? 3(3n?1)2 = 32n?1 ? 3n.

PDF	1 hw 6 (1) Let x1 ? R with x1 > 1 Define (xn) by xn+1 = 2 xn+1 = 2 ? 1 xn for n ? N Show that the sequence is monotone and bounded What is its limit? Proof For n = 1 x2 ? x1

PDF	447 HOMEWORK SET 6 1 33 3) Let x1 ? 2 and x n+1 := 1 + ? xn satisfies x =1+ ? x ? 1 ? x ? 1 = ? x ? 1 ? x ? {12} ? x = 2 since (xn) is bounded below by 2 0 4) Let x1 := 1 and xn+1 :=

PDF	1 Section 33 - 1 2 3 4 1 Section 3 3 - 1 2 3 4 1 1 Let x1 := 8 and xn+1 := 1 2 xn + 2 for n ? N Show that (xn) is bounded and monotone Find the limit

PDF	Answer to Question 𔈷 in Real Analysis for Zaighum abbas ii) let X1>1 and Xn+1=2-1/Xn for all n belongs to N Show that (Xn) is bounded and monotone Find the limits 1 Expert's answer

PDF	Practice Problems 2: Convergence of sequences and monotone n + 1 n xn) converges then (xn) converges 7 Show that the sequence (xn) is bounded and monotone and find its limit where (a) x1 = 2 and xn+1 = 2 ? 1

PDF	Solved Let x1 > 1 and xn+1 := 2?1/xn for n ? N Show that xn - Chegg Answer to Solved Let x1 > 1 and xn+1 := 2?1/xn for n ? N Show that xn

PDF	Solutions to Homework 6- MAT319 10 nov 2008 · Let x1 = 1 and xn+1 = ? 2 + xn Then lim xn = 2 Following the example set sn+1 = 1/2(sn +5/sn) and s1 = 5 Then s2 = 3

PDF	CUHK Mathematics - The Chinese University of Hong Kong From the recursive formula we see that L = 2 ? 1 L which is equivalent to the equation (L ? 1)2 = 0 We find that the limit of (xn) is 1 7 Let x1 := a

PDF	University of Illinois at Urbana-Champaign 1 n is not convergent Correction One has x2n = 1 2n and x2n+1 =2+ 1 (b) Let x1 ? 2 and xn+1 = 1+ ? xn ? 1 Prove that (xn) is decreasing and

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PDF	447 HOMEWORK SET 6 1 33 3) Let x1 ≥ 2 and x n+1 := 1 + √ xn satisfies x =1+ √ x − 1 ⇔ x − 1 = √ x − 1 ⇔ x ∈ {1,2} ⇒ x = 2, since (xn) is bounded below by 2 0 4) Let x1 := 1 and xn+1 := √ 2 + xn,n ∈ N Show (xn)

PDF	1 Section 33 - 1, 2, 3, 4 Show that (xn) is bounded and monotone Find the limit Proof First, let's show that it is monotone (decreasing) Note that x1 = 8 > x2 =

PDF	Practice Problems 2: Convergence of sequences and monotone Let xn = (−1)n for all n ∈ N Show that the sequence (xn) does not converge 3 Let A be (a) x1 = 2 and xn+1 = 2 − 1 xnfor n ∈ N (b) x1 = √ 2 and xn+1 = √

PDF	Solutions to Homework 6- MAT319 - Stony Brook Mathematics 10 nov 2008 · 1 Section 3 3 Exercise 1 (# 4) Let x1 = 1 and xn+1 = √ 2 + xn Then lim xn = 2 Following the example, set sn+1 = 1/2(sn +5/sn), and s1 = 5

PDF	Solutions to Homework 6- MAT319 10 nov 2008 · 1 Section 3 3 Exercise 1 (# 4) Let x1 = 1 and xn+1 = √ 2 + xn Then lim xn = 2 Following the example, set sn+1 = 1/2(sn +5/sn), and s1 = 5

PDF	Solutions to Homework 7- MAT319 17 nov 2008 · Let x1 = 2 and xn+1 =2+1/xn Then xn is contractive, and lim xn =1+ √ 2 First let us show xn is contractive

PDF	MA 101 (Mathematics I) Hints/Solutions for Practice Problem Set - 2 (xn) such that the sequence (yn) is convergent, where yn = xn + 1 n Let f(x) = { ( x − 1)2 sin 1 (x−1)2 if 1 < x ≤ 2, 0 if x = 1 Clearly f : [1,2] → R is differentiable

PDF	MATH201 INTRODUCTION TO ANALYSIS Worksheet for week 6 Lecture sessions 1/2 Name: Tutorial Section: Student ID: 1 Suppose that (xn) is a convergent sequence and (yn + 1 n ) Let lim xn = x We know x1 ≥ 2, if xk ≥ 2, then xk+1 = 1+ √ xk − 1 ≥ 1+ √ 2 − 1 = 2 Hence xn ≥ 2 for all n ∈ N by

PDF	Homework 3 232 234 242 - Purdue Math (b) =⇒ limxn+1 = lim 1 4−xn = 1 4−lim xn ⇒ x = 1 4−x ⇒ x = 2 − √3 Let x1 = √2, and xn+1 = √2xn ∀n ≥ 1 Claim: If 0 < xn < 2 ⇒ 0 < xn < xn+1 < 2

PDF	Math 242: Principles of Analysis Fall 2016 Homework 3 Part B Show that the sequence x1 = 1, xn+1 = xn + 1 xn diverges (Hint: Suppose it did converge ) Solution Suppose xn converges Let a = lim xn Clearly xn > 0 for all

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