Prove the following identities involving Fibonacci numbers: $${F_n}^2 + {F_{n+1}}^2 = F_{2n+1}.$$ I am not sure how to work with the 2n's.
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Can you use Binet's formula? – J. W. Tanner May 03 '20 at 23:27
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It is answered here. – anumosh May 03 '20 at 23:29
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Also see a nice visual explanation here – Roy Sht May 03 '20 at 23:30
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You can use the matrix form or induction to prove it, or even use Binet's formula directly. – Gareth Ma May 03 '20 at 23:31