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Fibonacci sums (Posted on 2004-07-15) Difficulty: 3 of 5
The Fibonacci series 0, 1, 1, 2, 3, 5, 8, 13, in which each number is the sum of the two previous, is defined as F(0)=0, F(1)=1, and F(n)=F(n-1)+F(n-2) for n>1.

What is the sum of F(0)+F(1)+F(2)+...+F(k)?
What is the sum of F(0)^2+F(1)^2+F(2)^2+...+F(k)^2?

See The Solution Submitted by Federico Kereki    
Rating: 3.7143 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: what is being asked??? | Comment 4 of 13 |
(In reply to what is being asked??? by Jim)

It is asking for a formula relating these partial sums up to a given term k, to the value of k chosen--that is, as a function of k.  So for example if k is 5, the formula for the first question would give you 0+1+1+2+3+5 = 12.  The formula given so far for that is F(k+2); in this instance that is F(5+2)=F(7)=12.
  Posted by Charlie on 2004-07-15 22:00:20

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