2002 AIME I Problem 7

The Binomial Expansion is valid for exponents that are not integers. That is, for all real numbers x, y, and r with |x|>|y|,

$$(x+y)^{r}=x^{r}+r x^{r-1} y+\frac{r(r-1)}{2!} x^{r-2} y^{2}+\frac{r(r-1)(r-2)}{3!} x^{r-3} y^{3}+\ldots$$

What are the first three digits to the right of the decimal point in the decimal representation of \left(10^{2002}+1\right)^{10 / 7} ?