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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: Inelegant solution | Comment 2 of 13 |
(In reply to Inelegant solution by Bryan)

For the latter question F(k) * F(k+1) seems to work regardless of odd or even k.
  Posted by Charlie on 2004-07-15 15:35:57

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