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If \( A_{i} \) is the area bounded by \( \left|x-a_{i}\right|+|y|=b_{i}, i \in N \), where
\( \mathrm{P} \) \( a_{i+1}=a_{i}+\frac{3}{2} b_{i} \) and \( b_{i+1}=\frac{b_{i}}{2}, a_{1}=0, b_{1}=32 \), then
(1) \( A_{3}=128 \)
(2) \( A_{3}=256 \)
(3) \( \lim _{n \rightarrow \infty} \sum_{i=1}^{n} A_{i}=\frac{8}{3}(32)^{2} \)
(4) \( \lim _{n \rightarrow \infty} \sum_{i=1}^{n} A_{i}=\frac{4}{3}(16)^{2} \)
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