A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Math2400

  • one year ago

determine the sum of this series...i thought it was divergent but I guess it diverges cuz it says that it's not divergent

  • This Question is Closed
  1. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\sum_{n=1}^{\infty} \frac{ (-3)^{n-1} }{ 5^n}\]

  2. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @jim_thompson5910 would u be able to help me on this please?

  3. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    As a start, write the fraction in single exponent

  4. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\sum_{n=1}^{\infty} \frac{ (-3)^{n-1} }{ 5^n} = \sum_{n=1}^{\infty} \frac{ (-3)^{n} }{ (-3)5^n} = -\frac{1}{3}\sum_{n=1}^{\infty} \left(\frac{ -3 }{ 5}\right)^n\]

  5. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    next recall geometric series

  6. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a/(1 - r) ??

  7. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Yep

  8. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what would be r? this is where I'm confused

  9. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    r = the stuff under the exponent = -3/5

  10. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and for a i just plug in 1 into the equation?

  11. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and get that value?

  12. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    there is no equation

  13. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    for "a", just plugin n=1 into the general term of series

  14. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that's what i mean haha :)

  15. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    i kno, just making sure you see the difference between "equation" and "expression"

  16. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay i plugged everything in but it's zero??

  17. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    what do you get for first term, a ?

  18. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (-3)^(1-1)/5^1=0

  19. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Ah no, below is our slightly massaged series : \[-\frac{1}{3}\color{blue}{\sum_{n=1}^{\infty} \left(\frac{ -3 }{ 5}\right)^n}\] plugin \(n=1\), you get \(a_1 = -\frac{3}{5} \) \(r = -\frac{3}{5}\) so the infinite sum is \[\dfrac{-3/5}{1-(-3/5)}\] simplify

  20. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    -0.375

  21. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that's still not right tho haha

  22. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    looks good, don't forget that -1/3 in front

  23. Math2400
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    got it! thanks :)

  24. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    np

  25. 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.