Question

How would you explain to a student that 1*3*5*...(2n+1) = 1*3*5*...(2n-1)(2n+1)?

Answer 1

Specifically, they are having trouble seeing that
\[\frac{1\cdot3\cdot5\dotsm(2n+1)}{1\cdot3\cdot5\dotsm(2n-1)}=2n+1.\]