Prove that $F(1) + F(3) + F(5) + ... + F(2n-1) = F(2n)$ (These are Fibonacci numbers; $f(1) = 0$, $f(3) = 1$, $f(5) = 5$, etc.) I'm having trouble proving this with induction, I know how to prove the base case and present the induction hypothesis but I'm unfamiliar with proving series such as this. Any help would be great. :)

Hint: If you can use the that the sequence of Fibonacci numbers is defined by the recurrence relation $$F(n)=F(n-1)+F(n-2)$$ then you can prove it by induction, since $$\begin{align*}F(2(n+1))&=F(2n+2)\\&=F(2n+1)+F(2n)\\&=F(2n+1)+\underbrace{F(2n-1)+\ldots+F(5)+F(3)+F(1)}_{=F(2n) \text{ by induction hypothesis}}\end{align*}$$
