Math CentralQuandaries & Queries


Question from Thomas, a student:

Hey I have a question for a research topic that our teacher set us, It is regarding the sum of the squares of the fibonacci numbers.
1² = 1 x 1
1²+1² = 1 x 2
1²+1²+2² = 2 x 3
1²+1²+2²+3² = 3 x 5
1²+1²+2²+3²+5² = 5 x 8
The question says describe the pattern that exists and write a general formula that describes the relationship ilustrated above. I can see the pattern that is occuring but i cannot put this into a general formula.
Any help would be appreciated.
Thanks Tom

Hi Tom,

Are the numbers on the right hand side Fibonacci numbers? They look like
they might be nearby in the sequence too.


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