Good luck!Proving the Relationship between Fibonacci and Lucas Series

[Suk-Sci]

Fibonacci and lucas series...

Let a₁,a₂,a₃...,a_n be the numbers of fibonacci series...
Let b₁,b₂...b_n be the number of lucas series.

b_n=a_n-1 + a_n+1 for n\geq2

T.P.T : a_2n=a_n*b_n

 

[Raphie]

T.P.T : a_2n=a_n*b_n

Keep in mind the following two identities...

(Lucas_(n-1) + Lucas_(n+1))/5 = Fibonacci_n
Lucas_n = (Golden Ratio)^n + (-1)^n(Golden Ratio)^-n

... where the Golden Ratio = ((sqrt 5) + 1)/2

 

[dodo]

Hi, Suk-Sci,
you can substitute the given expression for the b's into the equation you want to prove; then you will have something only in terms of a's, that you can prove using induction.

If you want more help, try to show what you have done so far; that helps us help you. :)