Question 12
In the product
$$
\left(1 + \frac{1}{1}\right) \cdot \left(1 + \frac{1}{3}\right) \cdot \left(1 + \frac{1}{5}\right) \cdots \left(1 + \frac{1}{2n-1}\right)
$$
the denominators of the fractions are all odd numbers from $1$ to $(2n - 1)$. Is it possible to choose a natural number $n \gt 1$ such that this product would evaluate to an integer?
$$
\left(1 + \frac{1}{1}\right) \cdot \left(1 + \frac{1}{3}\right) \cdot \left(1 + \frac{1}{5}\right) \cdots \left(1 + \frac{1}{2n-1}\right)
$$
the denominators of the fractions are all odd numbers from $1$ to $(2n - 1)$. Is it possible to choose a natural number $n \gt 1$ such that this product would evaluate to an integer?