A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Help please?? Find the sum of the infinite series 1/3 +4/9 + 16/27+ 64/81+...if it exists

  • This Question is Closed
  1. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Looks like \[\sum\dfrac{4^n}{3^{n+1}}\]

  2. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\cdots=\dfrac{1}{3}\sum\dfrac{4^n}{3^n} =\dfrac{1}{3}\sum\left(\dfrac{4}{3}\right)^n\]

  3. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now do you think this series exists?

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

    yes?

  5. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, this is geometric series, right?

  6. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    And we have common ratio greater than 1.

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

    yeah but I need to know what the sum of the series is

  8. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    For any finite geometric series, formula is \[\sum_{i=1}^{n-1} r^i = \dfrac{1-r^n}{1-r}\]Right?

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

    I think so, but what do put in to get the answer? Can you help walk me through the steps? I'm really confused.

  10. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you know calculus?

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

    no

  12. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Really? ok well just take a look at \[\dfrac{1-r^n}{1-r}\] Since common ratio (r) is greater than 1, what would happen to it if n getting bigger and bigger? \(r^n\) would get bigger and bigger, right?

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

    yes

  14. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well, so when you "get" to infinity. You would have infinity in numerator.

  15. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So this series doesn't exist.

  16. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Does that make sense?

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

    Okay thank you <3

  18. 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.