The given mathematical expression is:

$\text{lim}_{n \to \infty} \frac{(1 - \sqrt{n})(1 - \sqrt{x}) \dots (1 - \sqrt[n]{x})}{(1 - x)^{n-1}}$

Where the expression involves the terms $1 - \sqrt{k}$ up to $1 - \sqrt[n]{x}$, and the denominator involves $1 - x$ raised to the power $n-1$.

Would you like me to:

1. Simplify this step-by-step?
2. Analyze the limit behavior as $n \to \infty$?
3. Provide a general solution or conclusion?

Let me know your preference.

Meanwhile, here are 5 related questions for further exploration:

1. How does $\sqrt[n]{x}$ behave as $n \to \infty$?
2. Why does the term $(1 - x)^{n-1}$ appear in the denominator?
3. What happens if $x > 1$ or $x = 1$?
4. How do logarithmic approximations simplify limit expressions?
5. Can this expression be related to series expansions?

Tip: Limits involving roots often simplify significantly by expanding terms using the binomial or Taylor series.