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apple_pi
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0I think by getting a general term....

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

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

mukushla
 2 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
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0@phi this whole thing hinges upon you :D

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

apple_pi
 2 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
 2 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
 2 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
 2 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
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