Thanks, once I realized I could substitute for F(n+k) it was all downhill from there.
One question, when writing an induction proof for equations like this with two variables (n and k), should you prove 'n+1' or 'k+1'? Or both?
Homework Statement
Use induction to prove this equation:
F(n+k) = F(k)F(n+1) + F(k-1)F(n)
Homework Equations
F(0)=0 and F(1)=1
F(n)=F(n-1)+F(n-2)
The Attempt at a Solution
Base: n=0, k=1
F(1)=(1*1)+(0*0)=1
True for n=k
k=k+1
F(2k+1) = F(k)F(k+2) + F(k-1)F(k+1)...