$4 \cdot 224$ unit squares are divided into 9 equal parts by lines parallel to the sides, and the central part is removed. The remaining 8 smaller squares are each divided into 9 equal parts by lines parallel to the sides, and the central part is removed. Then, a similar process is applied to each of the remaining squares. If this process is repeated $n$ times, try to answer:
(1) How many squares with side length $\frac{1}{3^{n}}$ are there?
(2) What is the limit of the sum of the areas of the squares removed when $n$ is infinitely increased?

When the process is repeated $n$ times, try to answer:
(1) How many squares with side length $\frac{1}{3^{n}}$ are there?
(2) What is the limit of the sum of the areas of the squares removed when $n$ is infinitely increased?
［Solution］（1）After the first division and removing one square from the resulting 9 squares, 8 squares with a side length of $\frac{1}{3}$ remain; after the second division, $8 \times 9$ squares are obtained, from which 8 squares are removed, leaving $8^{2}$ squares with a side length of $\frac{1}{3^{2}}$; if this process is repeated $n$ times, then after the $n$-th division and removal, $8^{n}$ squares with a side length of $\frac{1}{3^{n}}$ will remain. As shown in the figure.
(2) The sum of the areas of the remaining squares after the $n$-th division is
$$8^{n}\left(\frac{1}{3^{n}}\right)^{2}=\left(\frac{8}{9}\right)^{n}$$

Therefore, the sum of the areas of the removed squares is $1-\left(\frac{8}{9}\right)^{n}$.
Since $\left(\frac{8}{9}\right)^{n}$ can be arbitrarily small when $n$ is sufficiently large, the sum of the areas of the removed squares approaches 1 as $n$ increases indefinitely.