Question

Let a1= - 1 , an+1= (6+an) / (2+an). a) Assume that the given recursive sequence...

Let a1= - 1 , an+1= (6+an) / (2+an).

a) Assume that the given recursive sequence is convergent. Find the limit.

b) Is the given sequence bounded? Why?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the following. a1 = 8, an + 1 = 9 − an Calculate, to four...
Consider the following. a1 = 8, an + 1 = 9 − an Calculate, to four decimal places, the first eight terms of the recursive sequence. Does it appear to be convergent? Yes No      If so, guess the value of the limit. (If the quantity diverges, enter DIVERGES.) Assume the limit exists and determine its exact value. (If the quantity diverges, enter DIVERGES.) lim n→∞ an = Consider the following. a1 = 1, an + 1 = square root (4an)...
A sequence has a recursive formula of an = (-2)n (an-1) for n≥2. The fourth term...
A sequence has a recursive formula of an = (-2)n (an-1) for n≥2. The fourth term a4 is 1,536. a. Find the first term a1. (5 points) b. Find the sixth term a6. (5 points)
Find a general term (as a function of the variable n) for the sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}. Find a...
Find a general term (as a function of the variable n) for the sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}. Find a general term (as a function of the variable n) for the sequence {?1,?2,?3,?4,…}={4/5,16/25,64/125,256/625,…} an= Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. (If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it diverges without being infinity or negative infinity, state your answer...
Using the recursion formula an+1 = (3an - 2)^1/2, with a1 = 4/3, do the following...
Using the recursion formula an+1 = (3an - 2)^1/2, with a1 = 4/3, do the following by induction. a. Show the sequence { an } is monotone increasing. b. Show the sequence is bounded above by 2. c. Evaluate the the limit of the sequence.
Let (a_n)∞n=1 be a sequence defined recursively by a1 = 1, a_n+1 = sqrt(3a_n) for n...
Let (a_n)∞n=1 be a sequence defined recursively by a1 = 1, a_n+1 = sqrt(3a_n) for n ≥ 1. we know that the sequence converges. Find its limit. Hint: You may make use of the property that lim n→∞ b_n = lim n→∞ b_n if a sequence (b_n)∞n=1 converges to a positive real number.  
A sequence is defined by a1=2 and an=3an-1+1. Find the sum a1+a2+⋯+an
A sequence is defined by a1=2 and an=3an-1+1. Find the sum a1+a2+⋯+an
Question 3. Let a1,...,an ∈R. Prove that (a1 + a2 + ... + an)2 /n ≤...
Question 3. Let a1,...,an ∈R. Prove that (a1 + a2 + ... + an)2 /n ≤ (a1)2 + (a2)2 + ... + (an)2. Question 5. Let S ⊆R and T ⊆R be non-empty. Suppose that s ≤ t for all s ∈ S and t ∈ T. Prove that sup(S) ≤ inf(T). Question 6. Let S ⊆ R and T ⊆ R. Suppose that S is bounded above and T is bounded below. Let U = {t−s|t ∈ T, s...
1. Find the limit of the sequence whose terms are given by an= (n^2)(1-cos(5.6/n)) 2. for...
1. Find the limit of the sequence whose terms are given by an= (n^2)(1-cos(5.6/n)) 2. for the sequence an= 2(an-1 - 2) and a1=3 the first term is? the second term is? the third term is? the forth term is? the fifth term is?
We are given a sequence of numbers: 1, 3, 5, 7, 9, . . . and...
We are given a sequence of numbers: 1, 3, 5, 7, 9, . . . and want to prove that the closed formula for the sequence is an = 2n – 1.          What would the next number in the sequence be? What is the recursive formula for the sequence? Is the closed formula true for a1? What about a2? What about a3? Critical Thinking How many values would we have to check before we could be sure that the...
Give a recursive description of the sequence of increasing even numbers 2, 4, 6, ...
Give a recursive description of the sequence of increasing even numbers 2, 4, 6, ...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT