Use Proof By Induction to find the product of consecutive odd integers up to $2n-1$

Question

I'm a bit stuck on this inductive proof. I have to find what this is equal to. Product of $1 \times 3 \times 5 \times \ldots \times (2n-1)$ Starting with $i= 1$. What would be a good starting point?

Answer 1

Hint: Whatever $$\prod_{k=1}^n(2k-1)$$ is, if we multiply it by $$\prod_{k=1}^n(2k),$$ then we'll end up with $(2n)!$ as a product. Try simplifying the second expression, so that you can get an explicit expression for the first.