Assume that the sequence defined by a1 = 3 an+1 = 15-2·an is decreasing and an...
Given that the sequence defined by - 1 2+1 = 5-1 an is increasing and an < 5 for all n. Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
3. (14 pts.) Let the sequence an be defined by ao = -2, a1 = 38 and an = 2an-1 + 15an-2 for all integers n > 2. Prove that for every integer n > 0, an = 4(5") + 2(-3)n+1.
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 =
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...
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
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = n^4/n^3 − 4n lim n→∞ 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.) 5n =tan 3 + 20n a. n
A sequence {an , is defined by the following formula. What is the limit of this sequence? do = 3, an= 3an-1-2, for n> 1.
Let a1 = 3 and an+1 = a + 5 2an for all n > 1 Prove that (an)nen converges and find limn7oo an: