Question

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.

Answer 1

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