I've been stuck on this one for quite some time now and would really appreciate a little hint. Let $\displaystyle F_i $ be the $\displaystyle i^{th} $ Fibonacci number. Show that $\displaystyle F_{2n} = F_{n+1}^2+F_{n-1}^2 $
Follow Math Help Forum on Facebook and Google+
I believe that identity is $\displaystyle F_{2n}=F^{2}_{n+1}-F^{2}_{n-1}$ You have a plus. Perhaps that is why you are having trouble. $\displaystyle F_{n+1}^{2}-F_{n-1}^{2}=\left(F_{n+1}-F_{n-1}\right)\left(F_{n+1}+F_{n-1}\right)$
whoops, thats what I meant, where do I go from here?
View Tag Cloud