Q:

Mathematical Induction (product of $n$ consecutive numbers)

Assumption:
$$(n+1)(n+2) \cdots (2n) = (2^n)\cdot 1 \cdot 3 \cdot 5 \cdots (2n-1)$$
Prove for $n+1$:
$$(n+2)(n+3) \cdots (2(n+1)) = (2^{n+1}) \cdot 1 \cdot 3 \cdot 5 \cdots (2(n+1)-1)$$
Using the assumption, I divide both sides by $(n+1)$ and substitute RHS into my $n+1$ equation, however it does not equate.

A:

My approach would be to "massage" the assumed equation to look more like the desired equation.
Hint:  Try multiplying the assumed equation by 2.  What's missing from the left side after this step?  What's missing from the right side?

