$\lim_{n \to \infty} \frac{\sqrt[n]{(1+n)(2+n)(3+n)...(2n)}}{n}$
Found this problem while studying for an upcoming Calculus test. The answer is $\frac{4}{e}$. However, I've been stuck on how to get to that result. I can't use integrals, Riemann sums, or Stirling's approximation, since we haven't been taught that yet. Intuition and the presence of $e$ tells me I have to algebraically turn it into some sort of indeterminate form (perhaps $1^∞$), but I haven't been able to.
