any help on getting started would be great. i really don't know where to go with this as i'm useless with limits.

alpha is the golden ration ((1+sqrt5)/2)

f2k etc are part of the fibonacci sequence

prove lim f2k/f2k+1 = 1/alpha

k->infinity

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- Feb 8th 2011, 12:55 PMgpenguinfibonacci and the golden ratio proof
any help on getting started would be great. i really don't know where to go with this as i'm useless with limits.

alpha is the golden ration ((1+sqrt5)/2)

f2k etc are part of the fibonacci sequence

prove lim f2k/f2k+1 = 1/alpha

k->infinity - Feb 8th 2011, 01:13 PMAckbeet
The Fibonacci sequence can be written as a recurrence relation. Solve that relation for the nth term, and then form the desired ratio and take the limit. Does that give you some ideas?

- Feb 8th 2011, 01:19 PMpickslides
Here's a hint: The golden ratio is the solution to the equation

Now look at the recurrence relationship of Fibonacci numbers, can you find this equation? - Feb 9th 2011, 01:44 PMchisigma