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What did I do wrong in the proof by mathematical induction of $f_{2n+1}=f^2_{n+1}+f^2_n$?

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marked as duplicate by dxiv, GNUSupporter 8964民主女神 地下教會, Yuriy S, Jack D'Aurizio Jan 22 '18 at 19:46

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    $\begingroup$ Please do not use pictures for critical portions of your post. Pictures may not be legible, cannot be searched and are not view-able to some, such as those who use screen readers. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Jan 22 '18 at 19:34
  • $\begingroup$ @dxiv Yes, but in that example they proof by n=k, and i want to prove it by n=k+1 $\endgroup$ – WinstonCherf Jan 22 '18 at 19:43
  • $\begingroup$ When $n=k+1$, you get $f_{2k+3}$, not $f_{2k+2}$. $\endgroup$ – user491874 Jan 22 '18 at 19:43
  • $\begingroup$ @user8734617 Yes, correct! $\endgroup$ – WinstonCherf Jan 22 '18 at 19:44
  • $\begingroup$ @LeneCoenen Not sure what you mean by that. It's the same identity, and the question has a number of answers posted. See more duplicates here and here for example. $\endgroup$ – dxiv Jan 22 '18 at 19:50

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