Given that the sequence defined by - 1 2+1 = 5-1 an is increasing and an...
Assume that the sequence defined by a1 = 3 an+1 = 15-2·an is decreasing and an > O for all n. Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) a, = 5 + 8n2 " n + 8n2 lim n >00 an = Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = e-9/vñ lim n >00 an =
4. Show that the sequence defined by a=2 An+1- 3-an satisfies () < an < 2 and is decreasing. Deduce that the sequence is convergent and find its limit.
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
n²5 Determine whether the sequence defined by a, 56m2 + 1 converges or diverges. If it converges, find its limit. O1 OS 6 Diverges
(1) Does there exist a sequence of 10100 consecutive composite numbers? (2) Let Pn be the nth prime number. Show that pn < 22".
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
005 10.0 points Determine whether the sequence {an} con- verges or diverges when en = (-1)" (5n+) (5n+7) (5n+4) and if it does, find its limit. 1. sequence diverges 2. limit = 0 3. limit = +1 4. limit 5. limit = 1 006 10.0 points Which of the following sequences converge? A. _2n | 3n +4J 4en +6) 5n+6 C. {_3en1 C. (4+2en) 1. A and C only 2. B only 3. none of them 4. A, B, and...
Exercises 4.2 ove that the sequence (1 + z/n)"; n = 1, 2, 3,..., converges uni- ly in Iz <R < , for every R. What is the limit? 1, afdos se converge? diverge?
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) = cos(n) lim an = n00