Question 21
What is the smallest positive odd integer $n$ such that the product $$
2^{\frac{1}{7}}2^{\frac{3}{7}}\cdots2^{\frac{2n+1}{7}}
$$ is greater than $1000?$ (In the product the denominators of the exponents are all sevens, and the numerators are the successive odd integers from $1$ to $2n+1.$)
2^{\frac{1}{7}}2^{\frac{3}{7}}\cdots2^{\frac{2n+1}{7}}
$$ is greater than $1000?$ (In the product the denominators of the exponents are all sevens, and the numerators are the successive odd integers from $1$ to $2n+1.$)