Fibonacci Numbers

posted by .

I posted the question several days ago and Mathmate helped to guide me along. I am just unsure if I do not understand what he is saying or if I did complete the problem right. I would appreciate any input.

1.618034 - -.618034 = 2.236068/sqrt 5 = 1.00000

I understand how to use a calculator to write the decimal point using the golden ratio which is 1.618034 and the conjugate is -.618034. I also know that the relationship between the decimal expansions is that everything to the right of the decimal is the same except one is neg. and one is pos.

Now I have a problem. I have to use the Binet form to calculate the 20th Fib. number. I can use my decimals that I used in the problem above, but I am not sure how to do this. I have worked out the Fibonacci numbers and found that the 20th number is 6,765.
I could really use some help in understanding my problem.

  • Fibonacci Numbers -

    Using Binet's formula,

    F(20) = ((1+√5)^20 - (1-√5)^20)/(√5 * 2^20)

    1+√5 = 3.236068
    1-√5 = -1.236068

    3.236068^20 = 1.5861811E10
    1.236068^20 = 69.31819834

    so, F(20) = 6765

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. linear analysis

    how do i solve for y(x) if dy/dx=x+y and y(0)=1 I know the answer is y(x)=2e^x-x-1 I posted this question before but i can't find my question so i would appreciate if you helped me again.
  2. grade 12 accounting

    I posted a question a while ago, I was hoping someone would get back to it?
  3. Computer Science

    For MathMate: Mythical Man Ques. You answered my ques. several days ago, but I do not quite understand the answer. The ques. was as follows: If it took one person 3 months to make one quilt, why does it take 6 people four months to …
  4. trigonometry (MathMate)

    MathMate i would really appreciate if you can show me where the logarithms can be used.I know they are unnecessary and I already found the answer without them but i still have to show my work using logarithms and they just confuse …
  5. trigonometry (repost) Mathmate

    I want to start by saying thank you . You have no idea how much u have helped me understand logarithms, even better then the books i have (it poorly explains the subject of trigonometry let alone logarithms and antilog). Your last …
  6. Pre-Calc

    Find three examples of the Fibonacci sequence in nature. Write a paragraph for each example. For each example, address the following questions: How does the example relate to the Fibonacci sequence?
  7. Fibonacci numbers

    I have three problems to answer dealing with Fibonacci numbers. I understand the first two, but would like for reassurrance that they are correct and lost on the last one and could use some help. Thank you. 1. Fibonacci numbers can …
  8. Fibonacci Numbers: Understand one part not another

    I understand how to use a calculator to write the decimal point using the golden ratio which is 1.618034 and the conjugate is -.618034. I also know that the relationship between the decimal expansions is that everything to the right …
  9. Algebra 2

    Two days ago "Steve" helped me with this problem. I am grateful to him. I didn't get it and asked for him to help me again. He showed it to me again, but I needed more steps shown. Then I think he was finished for tutoring for the …
  10. Calculus

    Find the area of the region bounded by the curves y = x^(-1/2), y = x^(–2), y = 1, and y = 3. a) (1/2)(3)^1/2 + (4/3) b) 2*(3)^1/2 - (8/3) c) (1/2)(3)^1/2 - (32/3) d) 2*(3)^1/2 - (32/3) e) (8/3) - 2*(3)^1/2 So one thing that is throwing …

More Similar Questions