Question 75
Let $x$ be the smaller of the two solutions of the equation $x^{2}-4x+2=0$. What are the first three digits after the decimal point in the (base 10) writing of the number
$$
x+x^{2}+x^{3}+\cdots+x^{2009} ?
$$
$$
x+x^{2}+x^{3}+\cdots+x^{2009} ?
$$