Hi, we've been trying to prove this identity and can't quite see how its done. Any insights would be greatly appreciated. . .

$\displaystyle \text{where } \newline F_1 = 1 \newline F_2 = 1, \newline F_n = F_{n-1} + F_{n-2} \text{ for } n \geq 3 \newline \newline L_1 = 1 \newline L_n = F_{n+1} + F_{n-1} \text{ for } n \geq 2$

show that

$\displaystyle F_{2n} = F_n L_n$

Thanks, MD