Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

graydarl

  • 2 years ago

Can someone hlep me with this math problem? serie : an=(alpha*n)/(n+1), n>=1 (alpha is from R-real number). I must determine if the series is monotone and bouded thank you very much

  • This Question is Closed
  1. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i would try with \(\alpha =1\) first

  2. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    in this case you would get \(a_n=\frac{n}{n+1}\) which is bounded below by \(1\) since \(\frac{n}{n+1}<1\) for all \(n\) and \(\lim_{n\to \infty}\frac{n}{n+1}=1\)

  3. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i meant "bounded above by one" not below!

  4. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    it is monotone increasing as you can check by taking the derivative and seeing that is always positive

  5. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then try the general case with \(\alpha\)

  6. Fazeelayaz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes alpha* n/(n+1) limi\[\lim_{x \rightarrow \infty}{n/n+1}\] \[n/n(1+1/n)=1/(1+1/n)\] take limit to infinity \[1/(1+0)=1\] \[\alpha*1=alpha\]

  7. Fazeelayaz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the last term is alpha

  8. Fazeelayaz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the serries os monotone

  9. Fazeelayaz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the serries is also bounded below becaise it says n>1 soo first term is 1

  10. Fazeelayaz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    plz give me medal if i helped

  11. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.