(50g) Nth Fibonacci Number
03-02-2015, 02:11 AM
Post: #19
 Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: (50g) Nth Fibonacci Number
(02-27-2015 01:48 PM)rprosperi Wrote:  So it appears an ansatz is a postulated theorem for some behavior which works, but without knowing why?

It's easy to verify that the sequence $$x_n=\alpha\cdot\phi^n$$ satisfies the equation $$x_{n+2}=x_{n+1}+x_n$$: that's exactly how we calculate $$\phi$$.

However just from looking at the recurrence it's not obvious to use a geometric sequence.
In this case the ansatz is a hint that allows you to solve this problem without too much linear algebra. In other cases, it might be a trick that has been proved successfully elsewhere.

My discomfort was related to the fact that I probably couldn't motivate the ansatz enough.
However you seem to estimate the post all the same.

Cheers
Thomas
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 Messages In This Thread (50g) Nth Fibonacci Number - Eddie W. Shore - 02-21-2015, 03:31 PM RE: (50g) Nth Fibonacci Number - Gerald H - 02-22-2015, 09:48 AM RE: (50g) Nth Fibonacci Number - Joe Horn - 02-22-2015, 09:06 PM RE: (50g) Nth Fibonacci Number - Offroad - 02-23-2015, 03:07 AM RE: (50g) Nth Fibonacci Number - rprosperi - 02-26-2015, 01:42 PM RE: (50g) Nth Fibonacci Number - Han - 02-26-2015, 07:39 PM RE: (50g) Nth Fibonacci Number - rprosperi - 02-26-2015, 08:23 PM RE: (50g) Nth Fibonacci Number - Joe Horn - 02-26-2015, 10:19 PM RE: (50g) Nth Fibonacci Number - Thomas Klemm - 02-26-2015, 10:45 PM RE: (50g) Nth Fibonacci Number - Han - 02-27-2015, 03:29 AM RE: (50g) Nth Fibonacci Number - rprosperi - 02-27-2015, 01:31 PM RE: (50g) Nth Fibonacci Number - Thomas Klemm - 02-26-2015, 11:04 PM RE: (50g) Nth Fibonacci Number - Thomas Klemm - 02-27-2015, 05:10 AM RE: (50g) Nth Fibonacci Number - rprosperi - 02-27-2015, 01:43 PM RE: (50g) Nth Fibonacci Number - Thomas Klemm - 02-27-2015, 05:58 AM RE: (50g) Nth Fibonacci Number - rprosperi - 02-27-2015, 01:48 PM RE: (50g) Nth Fibonacci Number - Han - 02-27-2015, 02:22 PM RE: (50g) Nth Fibonacci Number - Gerald H - 02-27-2015, 03:27 PM RE: (50g) Nth Fibonacci Number - Thomas Klemm - 03-02-2015 02:11 AM

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