Question

Determine the limits of the following sequences. The prove your claims using an e - N...

Determine the limits of the following sequences. The prove your claims using an e - N argument.

a. an = n / (n2 + 1)

b. bn = (4n + 3) / (7n - 5)

c. cn = 1/n sin(n)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use L’Hopital’s Rule to determine if the following sequences converge or diverge. If the sequence converges,...
Use L’Hopital’s Rule to determine if the following sequences converge or diverge. If the sequence converges, what does it converge to? (a) an = (n^2+3n+5)/(n^2+e^n) (b) bn = (sin(n −1 ))/( n−1) (c) cn = ln(n)/ √n
Find the limits of the following sequences (please show your solution clearly.)  : cn=(1-1/n2)n , dn=(1+1/n)n^2
Find the limits of the following sequences (please show your solution clearly.)  : cn=(1-1/n2)n , dn=(1+1/n)n^2
Do the following sequences converge or diverge? If it converges, find its limit. a) an =...
Do the following sequences converge or diverge? If it converges, find its limit. a) an = (4n^3+3n-6) / (5n^26n+2) b) an = (3n^3+2n-6) / (4n^3+n^2+3n+1) c) an = (n sin n) / (n^2+4) d) an = (1/5)^n
1. Consider the sequences defined as follows.(an) =(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn) =(n2(−1)n)= (−1,4,−9,16, . . .).(i)...
1. Consider the sequences defined as follows.(an) =(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn) =(n2(−1)n)= (−1,4,−9,16, . . .).(i) For each sequence, give its lim sup and its lim inf. Show your reasoning; definitions are not required.(ii) For each sequence, determine its set of subsequential limits. Proofs are not required.
(1 point) The three series ∑An, ∑Bn, and ∑Cn have terms An=1/n^8,Bn=1/n^5,Cn=1/n. Use the Limit Comparison...
(1 point) The three series ∑An, ∑Bn, and ∑Cn have terms An=1/n^8,Bn=1/n^5,Cn=1/n. Use the Limit Comparison Test to compare the following series to any of the above series. For each of the series below, you must enter two letters. The first is the letter (A,B, or C) of the series above that it can be legally compared to with the Limit Comparison Test. The second is C if the given series converges, or D if it diverges. So for instance,...
Please prove the following (using epsilon/delta proofs) formally and clearly: For Xn given by the following,...
Please prove the following (using epsilon/delta proofs) formally and clearly: For Xn given by the following, prove the convergence or divergence of the sequence (Xn): a) Xn = n2/(2n2+1) b) Xn = (-1)n/(n+1) c) Xn = sin(n)/(n2+1)
Prove that the correctness of the following properties of the given recursive sequences. a) Given the...
Prove that the correctness of the following properties of the given recursive sequences. a) Given the sequence P(1) = 1, P(n) = 2∗P(n−1) for all n ≥ 1, prove that P(n) = 2n−1 for all n ≥ 1 b) Given the sequence P(1) = 1, P(2) = 1, P(3) = 1, P(4) = 1, P(n) = P(n − 2) + P(n − 4) for all n ≥ 5, prove that P(n) = P(n − 1) for all even positive integers...
2. Sequence Convergence¶ (To be answered in LaTex) Show that the following sequence limits using either...
2. Sequence Convergence¶ (To be answered in LaTex) Show that the following sequence limits using either an ?−?ε−δ argument a) lim (3?+1) / (2?+5) = 3/2 answer in LaTex b) lim (2?) / (n+2) =2   answer in LaTex c) lim [(1/?) − 1/(?+1)] = 0 answer in LaTex
Determine whether the following sequences converge or diverge. If it converges, find the limit. Must show...
Determine whether the following sequences converge or diverge. If it converges, find the limit. Must show work 1.)an = nsin(1/n) 2.)an = sin(n) 3).an =4^n /1 + 9^n 4).an = ln(n+1) − ln(n)
Examine if the following student definitions clearly capture all sequences that have limits and clearly exclude...
Examine if the following student definitions clearly capture all sequences that have limits and clearly exclude all sequences that don’t have limits. Explain how you can tell. (a) Amy’s definition L is a limit of a sequence {an}∞ n=1 if and only if an approaches L as n approaches ∞. (b) Brittany’s definition L is a limit of a sequence {an}∞ n=1 if and only if an gets closer to but never reaches L as n approaches ∞. (c) Cindy’s...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT