hello people. can someone please solve this using "mathematical induction" ????? thank you very much
it's obviously true for n = 1. suppose the claim is true for n, i.e. $\displaystyle f_{n+1}f_{n-1}-f_n^2=(-1)^n.$ now we have:
$\displaystyle f_{n+2}f_n - f_{n+1}^2=(f_n+f_{n+1})(f_{n+1}-f_{n-1})-f_{n+1}^2=f_n(f_{n+1}-f_{n-1})-f_{n+1}f_{n-1}$
$\displaystyle =f_n^2-f_{n+1}f_{n-1}=-(f_{n+1}f_{n-1}-f_n^2)=-(-1)^n=(-1)^{n+1}. \ \ \ \Box$
Thank you my friend. but saying the truth, I always had problems understanding the inductive method. now when it comes to Fibonacci, I feel like Im more in trouble. I am going to have my mid-term exam within 3 days
Can you please explain for me, the induction and also inductive proves for Fibonacci ? Thank U a lot