Prove the following identity: (F(n+1))^2 - (F(n))^2 = F(n-1)F(n+2) I am trying to do this with induction, and I am stuck!
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Originally Posted by veronicak5678 Prove the following identity: (F(n+1))^2 - (F(n))^2 = F(n-1)F(n+2) I am trying to do this with induction, and I am stuck! Merely note that . Noting then that and gives the desired result.
Originally Posted by veronicak5678 Prove the following identity: (F(n+1))^2 - (F(n))^2 = F(n-1)F(n+2) I am trying to do this with induction, and I am stuck! Alternatively (using induction to practice! given the clarity of Drexel's response) if then we require that Proof Therefore, is gives hence the hypothesis is true
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