Question

show that the sequence sin(n+2)/n is Cauchy

show that the sequence sin(n+2)/n is Cauchy

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
Exercise 2.4.5: Suppose that a Cauchy sequence {xn} is such that for every M ∈ N,...
Exercise 2.4.5: Suppose that a Cauchy sequence {xn} is such that for every M ∈ N, there exists a k ≥ M and an n ≥ M such that xk < 0 and xn > 0. Using simply the definition of a Cauchy sequence and of a convergent sequence, show that the sequence converges to 0.
Use the definition of a Cauchy sequence to prove that the sequence defined by xn =...
Use the definition of a Cauchy sequence to prove that the sequence defined by xn = (3/2)^n is a Cauchy sequence in R.
If Xn is a cauchy sequence and Yn is also a cauchy sequence, then prove that...
If Xn is a cauchy sequence and Yn is also a cauchy sequence, then prove that Xn+Yn is also a cauchy sequence
Prove that if a sequence is a Cauchy sequence, then it converges.
Prove that if a sequence is a Cauchy sequence, then it converges.
Suppose that every Cauchy sequence of X has a convergent subsequence in X. Show that X...
Suppose that every Cauchy sequence of X has a convergent subsequence in X. Show that X is complete.
Let the nth term of a sequence be given by an = sin(n2)/n for n ≥...
Let the nth term of a sequence be given by an = sin(n2)/n for n ≥ 1. 1. Is the sequence bounded? If so, by what values? 2. Is the sequence eventually monotone? If so, for what value of N is {an}∞n=N monotone? 3. Is the sequence increasing? Decreasing?
Let (xn) be Cauchy in (M, d) and a ∈ M. Show that the sequence d(xn,...
Let (xn) be Cauchy in (M, d) and a ∈ M. Show that the sequence d(xn, a) converges in R. (Note: It is not given that xn converges to a. Hint: Use Reverse triangle inequality.)
Question 4 Let a sequence {an}∞ n=1 a sequence satisfying the condition ∀c ∈ (0, 1),...
Question 4 Let a sequence {an}∞ n=1 a sequence satisfying the condition ∀c ∈ (0, 1), ∀n ∈ N, | a_(n+2) − a_(n+1) | < c |a_(n+1) − a_n |. 4.1 Show that ∀c ∈ (0, 1), ∀n ∈ N, n ≥ 2, | a_(n+1) − a_n | < c^(n−1) | a_2 − a_1 |. 4.2 Show that {an}∞ n=1 is a Cauchy sequence
I am trying to prove that (sn) is a Cauchy sequence where |sn+1-sn| < 2-n. So...
I am trying to prove that (sn) is a Cauchy sequence where |sn+1-sn| < 2-n. So far, I have figured out that |sm-sn| <= 1/2m+1 + 1/2m+2 + ... + 1/2n. I want to try to not use the geometric series condition. My professor hinted that the right hand side is less than 2/2n but I'm not sure how to find that or how to go from here!
if {Xn} and {Yn} are cauchy, show that {Xn +Yn} is cauchy. b.) Also show that...
if {Xn} and {Yn} are cauchy, show that {Xn +Yn} is cauchy. b.) Also show that {XnYn} is cauchy
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT