Answer
1000
Work Step by Step
When we plug in 1 into $\frac{x^{1000} -1}{x-1}$, we see that the result is $\frac{0}{0}$, an indeterminate form. This means we have to use L'Hospital's rule to evaluate the limit.
Using L'hospital's rule and the power rule for polynomials:
$$\frac{\frac{d}{dx}x^{1000}-1}{\frac{d}{dx}x-1} = \frac{1000x^{999}}{1}$$
Now, since we are taking the limit of a continuous polynomial, we can plug in 1 to find the answer. $$\lim\limits_{x \to 1}\frac{1000x^{999}}{1}=1000\times1^{999}=1000$$
