Question

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!

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

Homework Answers

Answer #1

Note. I'm not sure what is meant by |sn+1-sn|< 2-n. According to my judgement, it might be

Case 1. , in which case the solution is given below.

Case 2. , in this case {} is not a Cauchy sequence at all. Suitable counter example is given.

Case 3. , which is not possible as for n > 2, it would imply that a non negative number is less than 0, which is certainly not possible.

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
Hi I am trying to prove this statement but I'm not sure how to go about...
Hi I am trying to prove this statement but I'm not sure how to go about doing so. The statement is: Let q be greater than or equal to 2 be a positive integer. If for all integers a and a,whenever q|ab, q|a, or q|b, then q is prime.
I'm trying to solve for sequence and series question. The sequence goes from n=2 to infinity...
I'm trying to solve for sequence and series question. The sequence goes from n=2 to infinity and an = 1/n(ln(n))4/3. I've been trying to figure out using limit form of comparison test. However, when I used 1/n or 1/ln(n) as ab I get convergence and 1/n and 1/ln(n) are both divergent by proof.
Show that the series \sum_{n=1}^{\infty} 1/(x^2 + n^2) defines a differentiable function f: R -> R...
Show that the series \sum_{n=1}^{\infty} 1/(x^2 + n^2) defines a differentiable function f: R -> R for which f' is continuous. I'm thinking about using Cauchy Criterion to solve it, but I got stuck at trying to find the N such that the sequence of the partial sum from m+1 to n is bounded by epsilon
Read the following letter and answer the questions: Dear Sir: I am writing in response to...
Read the following letter and answer the questions: Dear Sir: I am writing in response to your request for additional information in Block #3 of the accident reporting form. I put “Poor Planning” as the cause of my accident. You said in your letter that I should explain more fully and I trust that the following details will be sufficient. I am a bricklayer by trade. On the day of the accident, I was working alone on the roof of...
I'm working in a 6 page research paper and below is the complete list of the...
I'm working in a 6 page research paper and below is the complete list of the paper has to be set up and the required things needed to be included. Can you check to see what is already included on the list and what is missing in my paper. Also, what I need to improve and how? My topic is "The Struggles of Epilepsy". Can you help me with the content (background, empirical research, and hypothesis )? I also need...
1. Summarize in a few sentences what Ayers found about pricing strategies in car markets. 2....
1. Summarize in a few sentences what Ayers found about pricing strategies in car markets. 2. Do you think that this is a profit maximizing strategy? Do you think this is an appropriate and reasonable strategy for businesses to undertake it it increases their profits? 3. Can you think of other goods or services that could be - or are - priced the same way? Check out the article on discrimination in coffee shops "Waiting for Good Joe" for some...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT