We define the sequence:

Prove that:

A nice identity indeed :D , it turned out to be a bit of a surprise really :eek:

Go ahead, it's your turn to prove it

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- Jan 5th 2008, 02:53 AMPaulRSFibonacci numbers
We define the sequence:

Prove that:

A nice identity indeed :D , it turned out to be a bit of a surprise really :eek:

Go ahead, it's your turn to prove it - Aug 31st 2009, 12:36 AMgirdav
Let

We have so

and ,

Now we can show the result by induction:

and

Assume that

- Aug 31st 2009, 11:12 AMNonCommAlg
a result of this problem is this identity: because: where

and - Sep 1st 2009, 12:03 AMsimplependulum
I prefer to use this complicated ( depends on you ) method (Happy)

and consider

and

is the differential operator

sum of them :

multiply

compare the coefficient of

from the left hand side : we obtain the series from your question

from the right hand side :