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29. Determine whether the sequence is monotone or not: otone or not: (6720) A. Monotone Increasing...
show all work | 2n-1) 2. Consider the sequence |(n+1)! a) is the sequence monotone increasing or monotone decreasing or neither? b) Find upper and lower bounds for the sequence. c) Does the sequence converge or diverge? (Explain) 3. Determine if the series converges or diverges. If it converges, find its sum. => [-1-] c) Ë ?j? – 1-1 j? +1
Show that a bounded and monotone sequence converges. Here a sequence is called monotone, if it is either monotone increasing, that is for all or monotone decreasing, in which case for all . in Sn=1 An+1 > an neN an+1 < an We were unable to transcribe this image
4. Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded? 3n - 7 a) b) an 7n+ 5 2 пл an = COS
Question 2. Monotone Convergence Define a sequence (an) inductively by ai = 1 and an+1 = ("p) (a) Show that, for any k E N, if 0 <a << 2 then 0 < ak+1 <2, and deduce that a, E (0,2) for all E N (b) Show that the sequence (an) is increasing and bounded above. (c) Prove that the sequence converges, and find its limit Question 2. Monotone Convergence Define a sequence (an) inductively by ai = 1 and...
(9 marks) Let { ln(n+11) n+3 }n=1 be a sequence. a. Find the first 5 terms of the sequence in the exact form. b. Determine whether the sequence is strictly monotone, monotone, eventually strictly monotone, eventually monotone or neither. Prove it. c. Determine whether the sequence is convergent, and if so, find its limit.
show that the sequence is eventually decreasing or increasing. and determine the smallest value of n for which the term is decreasing or increasing. (b) {
Determine if the next sequence is monotonous. If so, indicate if it is increasing, decreasing, not increasing or not decreasing. Www In(n+3) n + 3
1. Determine an infinite sequence that satisfies the following ... (a) An infinite sequence that is bounded below, decreasing, and convergent (b) An infinite sequence that is bounded above and divergent (c) An infinite sequence that is monotonic and converges to 1 as n → (d) An infinite sequence that is neither increasing nor decreasing and converges to 0 as n + 2. Given the recurrence relation an = 0n-1 +n for n > 2 where a = 1, find...
3. Give an example of a sequence {sn} that is not monotone, but the se- quence {s} is monotone. (7 points) carlo ST 4. Let $i = 4 and 9n+1 = (38m + 1)/5 for n 2 1. Show that the sequence {sn} is bounded and monotone, and find its limit s. (10 points)
H-4-2. [5 marks] (a) Consider the sequence (2n 1)I and determine whether it is (eventually) (strictly) increasing or (eventually) (strictly) decreasing or not monotonic. YOU DON'T HAVE TO COMPUTE ANY LIMITS (b) Consider the sequence [10n -3"} and determine whether it is (eventually) (strictly) increasing or (eventually) (strictly) decreasing or not monotonic. YOU DONT HAVE TO COMPUTE ANY LIMITS Grading. M2 S1 R1 Cl