Let $L_n$ be the Lucas numbers, defined by $L_n = F_{n-1} + F_{n+1}$ where f is the Fibonacci numbers.
How to prove that
$L_{2n+1} = \displaystyle \sum_{k=0}^{\lfloor n + 1/2\rfloor}\frac{2n+1}{2n+1 - k}{2n+1 - k \choose k} $
Let $L_n$ be the Lucas numbers, defined by $L_n = F_{n-1} + F_{n+1}$ where f is the Fibonacci numbers.
How to prove that
$L_{2n+1} = \displaystyle \sum_{k=0}^{\lfloor n + 1/2\rfloor}\frac{2n+1}{2n+1 - k}{2n+1 - k \choose k} $