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Sauda,c~oes,
Escrevi para o prof. Rousseau sobre este problema. Segue sua
resposta.
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Dear Luis:
Thanks for the problem. My recollection is that finding
(an exact
expression) for the sum of reciprocals of Fibonacci numbers is
a (famous?) unsolved problem. Of course, the second
part is
easier. For that, one can just compute an appropriate
partial
sum where the corresponding tail is shown to be
appropriately small, for
example by using Binet's formula.
I just got your message, so I haven't
carried
out the details of (2), but I know that I don't have any useful
ideas about (1). I will take a look at the site you mentioned.
Cheers,
Cecil
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Ficamos ent�o com o problema de resolver a segunda parte.
E se ajudar, a f�rmula de Binet �: F(n) = c ( A^n - B^n ),
onde c = sqrt{5}/5, A = (1 + sqrt{5})/2 e B = (1 - sqrt{5})/2
[ ]'s
Lu'is
Enviada em: Sexta-feira, 13 de Abril de
2001 21:40
Assunto: Parte inteira - insistente
Primeia parte : Qual � o limite de somat�rio de
1/F(n) com n variando de 1 at� G , onde F(n) � o n-�simo da sequ�ncia de
Fibonacci, com G tendendo a infinito ??
Segunda parte : Se o limite n�o for infinito, e �
igual a H, calcular a parte inteira de 50H.
Abra�os,
� Villard
!
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