I can't seem to figure out this proof. I'm using weak induction and always get stuck during the inductive step.
Prove for n > 0: $$f_{2n+1} = f_{n+1}^2 + f_n^2$$
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1Hi. See this page for info about writing mathematical formulas on this site (and you can also press edit on questions to see how the formulas have been written). – Winther Sep 15 '14 at 17:44
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1Are you required to use weak induction for this exercise? Have you tried using strong induction? – hardmath Sep 15 '14 at 17:48
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2The formula is derived here – Thomas Sep 15 '14 at 17:54
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Besides the obvious proof by induction, this can also be proved using the explicit formula for the Fibonacci sequence. – Yuval Filmus Sep 15 '14 at 17:59