MathDB

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 \plus{} y)^r \equal{} x^r \plus{} rx^{r \minus{} 1}y \plus{} \frac {r(r \minus{} 1)}2x^{r \minus{} 2}y^2 \plus{} \frac {r(r \minus{} 1)(r \minus{} 2)}{3!}x^{r \minus{} 3}y^3 \plus{} \cdots What are the first three digits to the right of the decimal point in the decimal representation of \left(10^{2002} \plus{} 1\right)^{10/7}?

Problem Statement