1. **Stating the problem:** We want to find the limit of the sequence $$a_n=\frac{(n!)^{\frac{1}{n}}}{n}$$ as $$n$$ tends to infinity. 2. **Rewrite the expression:** $$a_n=\frac{(n!)^{\frac{1}{n}}}{n} = \frac{\exp\left(\frac{1}{n}\ln(n!)\right)}{n}$$ 3. **Apply Stirling's approximation:** For large $$n$$, $$\ln(n!)\approx n\ln n - n$$. 4. **Substitute into the expression:** $$a_n \approx \frac{\exp\left(\frac{1}{n}(n\ln n - n)\right)}{n} = \frac{\exp(\ln n - 1)}{n}$$ 5. **Simplify the exponent:** $$\exp(\ln n - 1) = \exp(\ln n) \cdot \exp(-1) = n e^{-1}$$ 6. **Therefore:** $$a_n \approx \frac{n e^{-1}}{n} = e^{-1} = \frac{1}{e}$$ 7. **Conclusion:** $$\lim_{n \to \infty} \frac{(n!)^{1/n}}{n} = \frac{1}{e}$$