[PDF] 447 HOMEWORK SET 6 1 33 3) Let x1 ≥ 2 and x n+1 := 1 + √ xn
1 3 3 3) Let x1 ≥ 2 and xn+1 := 1 + √ xn − 1,n ∈ N Show that (xn) is decreasing and bounded below by 2 Find the limit Solution We are given x1 ≥ 2
[PDF] Practice Problems 2: Convergence of sequences and monotone
2 Let xn = (−1)n for all n ∈ N Show that the sequence (xn) does not converge 3 (b) x1 = √ 2 and xn+1 = √ 2xn for n ∈ N (c) x1 = 1 and xn+1 = 4+3xn
[PDF] Math 3150 Fall 2015 HW2 Solutions
(c) By part (a), s = limsn ≥ a and by part (b) s ≤ b, so s ∈ [a, b] D Problem 2 Let x1 = 1 and xn+1 = 3x2 n for n ≥ 1 (a) Show if a = limxn, then a = 1 3 or a = 0
[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 First we show that xn is increasing by using an induction
[PDF] 1 Section 33 - 1, 2, 3, 4
1 Let x1 := 8 and xn+1 := 1 2 xn + 2 for n ∈ N Show that (xn) is bounded and monotone Find the limit Proof First, let's show that it is monotone (decreasing)
[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 Ex 2(g) Let x1 = 1 and xn+1 = ( n Ex 2(h) Let a, b ∈ R, x1 = a, x2 = b and xn+2 = 1 2 −3
[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 First we show that xn is increasing by using an induction
[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] PROBLEM SET 02: CONVERGENCE OF SEQUENCES AND
(1) Let (xn) be a sequence such that xn → x and xn → y bounded and monotone, and find its limit (a) x1 = 1 and xn+1 = 4+3xn 3+2xn (b) xn+1 = 1 2 ( xn + a
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