G4.2 Suppose $P(x)=a_{0}+a_{1} x+a_{2} x^{2}+\ldots+a_{8} x^{8}$ is a polynomial of degree 8 with real coefficients $a_{0}, a_{1}, \ldots, a_{8}$. If $P(k)=\frac{1}{k}$ when $k=1,2, \ldots, 9$, and $b=P(10)$, find the value of $b$.