Use induction to prove this equation:
F(n+k) = F(k)F(n+1) + F(k-1)F(n)
F(0)=0 and F(1)=1
The Attempt at a Solution
Base: n=0, k=1
True for n=k
F(2k+1) = F(k)F(k+2) + F(k-1)F(k+1)
Here is where I get stuck, I'm not sure how to manipulate this equation to show they are equal. I'm pretty sure I can solve it using only the relevant equations above.