Subject: Fibonacci's Sequence
What discoveries can be made about the sum of squares of Fibonacci's Sequence.
Middle School/Junior High
Planned use of the information:
Brief Research or Class AssignmentHi Vandan,
(fn)2 + (fn + 1)2 = f2n + 1
This fact follows from a more general result that states:
fafn + fa + 1fn + 1 = fa + n + 1
for all natural numbers n.
This can be proved by mathematical induction.
To get the previous result let a = n.