I4.4 Let $[x]$ be the largest integer not greater than $x$. For example, $[2.5]=2$.
Let $w=1+\left[10 \times s^{2}\right]+\left[10 \times s^{4}\right]+\left[10 \times s^{6}\right]+\ldots+\left[10 \times s^{2 n}\right]+\ldots$, find the value of $w$.
$\begin{aligned} w & =1+\left[10 \times \frac{1}{2}\right]+\left[10 \times \frac{1}{4}\right]+\left[10 \times \frac{1}{8}\right]+\ldots+\left[10 \times \frac{1}{2^{n}}\right]+\ldots \\ & =1+5+2+1+0+0+\ldots=9\end{aligned}$