Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

apple_pi

  • 2 years ago

1/89 (fibonacci)

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

    If you sum all the fibonacci numbers like this: 1 * 10^-2 + 1 * 10^-3 + 2 * 10^-4 + 3 * 10^-5 + 5 * 10^-6 + 8 * 10^-7 + ... You end up getting 1/89. How can this be proven?

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

    I think by getting a general term....

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

    This is called a geometric series (which are fortunately convergent). There is a formula s = 1/(1-r) where r is the ratio of the n+1 th term divided by the nth term

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

    you also know that the fibonacci series can be generalized by: T[n+2] = T[n] + T[n+1]

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

    So, T[n] = {T[n+2] - T[n+1]} * 10^(n-2)

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

    Sorry I made a mistake, Lizzardo is right :)

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

    are u familiar with this formula? \[\frac{1}{1-x-x^2}=\sum_{n=0}^{\infty } F_n x^n\]

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

    er, no

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

    when in doubt, try wikipedia see http://en.wikipedia.org/wiki/Fibonacci_number#Power_series

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

    @phi this whole thing hinges upon you :D

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

    @apple_pi now how would u solve this?

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

    in this case x = 0.1 so sum = 1/ (1-0.1-0.01) = 1/0.89 = 100/89 = 1.1235955... So do we divide by 100? and where did that come from?

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

    note that what u got is 1 * + 1 * 10^-1 + 2 * 10^-2 + 3 * 10^-3 + 5 * 10^-4 + 8 * 10^-5 + ... multiply it by 10^-2 to get ur answer

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

    First, the article derives the formula muk posted. but there is supposed to be an x up top which he left out. also, for your sequence, first factor a 0.1 out of your numbers, so that it matches the formula

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

    the formula in wiki starts at F0 =0 F1= 1 F2= 1 F3= 2 and so on

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

    Ok thanks

  17. 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.