# Mathematical induction: $f_{2n+1}=f^2_{n+1}+f^2_n$ [duplicate]

What did I do wrong in the proof by mathematical induction of $f_{2n+1}=f^2_{n+1}+f^2_n$?
• When $n=k+1$, you get $f_{2k+3}$, not $f_{2k+2}$. – user491874 Jan 22 '18 at 19:43