A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

find all the values of x such that the series converges 3(2x+1)^n, n=0 to infinity

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, i wrote out some values and ended up with -1\[-1<2x+1<1\]

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

    ignore the extra -1 besides "with" lol

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If x is greater than or equal to 1, then the function blows up at infinity and it diverges...and we know that for a geometric series (which is what we have), the absolute value of the ratio has to be less than one to converge. So, -1< (2x+1) <1 and -1 < x < 0 works.

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i did get -1, so wud the inequality be the final response\[-1<x <0\]?

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I believe so. :)

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

    It works.

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

    i dont think we can use the inequality as a value, so can we just stick with -1?

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

    the inequality is a range of values

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

    No, because you get 3*(-1)^n which is divergent - it just bounces up and down, 3 + 3 - 3 + 3... and it's not convergent upon any specific value.

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

    If you don't want to use an inequality, you can say that "The acceptable values of x for which the series converges lie within (-1,0)."

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    doesn't 0 work though? it might have to be (-1,0]

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah it does work :) i'll just write the inequality down

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No, 0 doesn't work because you get 3 * (1^n) which is 3 + 3 + 3 + 3... which is divergent.

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\lim_{n->\infty} 1^n = 1 \]

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3*(lim n-> inf 1^n) =3*1 = 3

  16. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It's true that the expression for a_n converges, but when you actually compute it you get a constant stream of 3 * (1+1+1+1+1+...) which diverges.

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh it's a_n = (3*(2(x) + 1)^n where we are summing up a_0 -> a_inf. My mistake

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks zaighum47 for all ur help, really apprectiate it :)

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.