perplexus.info :: Just Math : Fibonacci sums

Fibonacci sums (Posted on 2004-07-15)

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?

Submitted by Federico Kereki

Rating: 3.7143 (7 votes)

Solution: (Hide)

The first sum is F(k+2)-1; the second, F(k)×F(k+1). Both results are easily proved by induction.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution To Part B	K Sengupta	2007-05-31 06:14:01
Solution To Part A	K Sengupta	2007-05-31 06:12:27
intuition behind the solution for part II	Bon	2004-08-04 18:59:48
intuition behind the solution for part I	Bon	2004-08-04 18:34:07
solved by induction	Mohammad	2004-07-17 23:42:49
Part 1 solution + explanation	Tristan	2004-07-16 15:52:57
Marginally more elegant solution for Square	Hew BG	2004-07-16 07:25:19
More	Richard	2004-07-15 22:54:46
re(2): what is being asked???	Richard	2004-07-15 22:17:37
re: what is being asked???	Charlie	2004-07-15 22:00:20
what is being asked???	Jim	2004-07-15 15:45:34
re: Inelegant solution	Charlie	2004-07-15 15:35:57
Inelegant solution	Bryan	2004-07-15 14:53:26

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