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.
Asked
Active
Viewed 55 times
0
-
Can you use [Binet's formula](https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression)? – J. W. Tanner May 03 '20 at 23:27
-
It is answered [here](https://math.stackexchange.com/questions/300345/induction-proof-fibonacci-numbers-identity-with-sum-of-two-squares). – anumosh May 03 '20 at 23:29
-
Also see a nice visual explanation [here](https://math.stackexchange.com/questions/936383/remarkable-relation-between-fibonacci-numbers-and-its-squares/936594#936594) – Roy Sht May 03 '20 at 23:30
-
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