A community for students.
Here's the question you clicked on:
 0 viewing
apple_pi
 3 years ago
1/89 (fibonacci)
apple_pi
 3 years ago
1/89 (fibonacci)

This Question is Closed

apple_pi
 3 years ago
Best ResponseYou've already chosen the best response.0If 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?

Lizzardo
 3 years ago
Best ResponseYou've already chosen the best response.0I think by getting a general term....

Rowan
 3 years ago
Best ResponseYou've already chosen the best response.0This is called a geometric series (which are fortunately convergent). There is a formula s = 1/(1r) where r is the ratio of the n+1 th term divided by the nth term

Lizzardo
 3 years ago
Best ResponseYou've already chosen the best response.0you also know that the fibonacci series can be generalized by: T[n+2] = T[n] + T[n+1]

Lizzardo
 3 years ago
Best ResponseYou've already chosen the best response.0So, T[n] = {T[n+2]  T[n+1]} * 10^(n2)

Rowan
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry I made a mistake, Lizzardo is right :)

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1are u familiar with this formula? \[\frac{1}{1xx^2}=\sum_{n=0}^{\infty } F_n x^n\]

phi
 3 years ago
Best ResponseYou've already chosen the best response.0when in doubt, try wikipedia see http://en.wikipedia.org/wiki/Fibonacci_number#Power_series

apple_pi
 3 years ago
Best ResponseYou've already chosen the best response.0@phi this whole thing hinges upon you :D

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1@apple_pi now how would u solve this?

apple_pi
 3 years ago
Best ResponseYou've already chosen the best response.0in this case x = 0.1 so sum = 1/ (10.10.01) = 1/0.89 = 100/89 = 1.1235955... So do we divide by 100? and where did that come from?

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1note 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

phi
 3 years ago
Best ResponseYou've already chosen the best response.0First, 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

phi
 3 years ago
Best ResponseYou've already chosen the best response.0the formula in wiki starts at F0 =0 F1= 1 F2= 1 F3= 2 and so on
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.