9.7 Try to select 100 numbers, such that they satisfy
$$
\begin{array}{c}
x_{1}=1,0 \leqslant x_{k} \leqslant 2 x_{k-1}, k=2,3, \cdots, 100, \\
\text { and make } s=x_{1}-x_{2}+x_{3}-x_{4}+\cdots+x_{99}-x_{100} \text { as large as possible. }
\end{array}
$$
［Solution］ From the assumption, we have
$$
\begin{aligned}
s & \leqslant x_{1}+\left(-x_{2}+x_{3}\right)+\left(-x_{4}+x_{5}\right)+\cdots+\left(-x_{98}+x_{99}\right) \\
& \leqslant x_{1}+x_{2}+x_{4}+\cdots+x_{98} \\
& \leqslant 1+2+2^{3}+\cdots+2^{97} .
\end{aligned}
$$

From this, we know that $x_{1}=1, x_{2}=2, x_{3}=2^{2}, \cdots, x_{98}=2^{97}, x_{99}=2^{98}, x_{100}=0$ is the solution.