106指考數學乙試題-05

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<多選題>設 \( a_1, a_2, \cdots, a_n, \cdots \) 是一公比為 \(\frac{1}{2}\) 的無窮等比數列且 \(a_1 = 1\)。試問以下哪些數列會收斂？
(1) \(-a_1, -a_2, \cdots, -a_n, \cdots\)
(2) \(a_1^2, a_2^2, \cdots, a_n^2, \cdots\)
(3) \(\sqrt{a_1}, \sqrt{a_2}, \cdots, \sqrt{a_n}, \cdots\)
(4) \(\frac{1}{a_1}, \frac{1}{a_2}, \cdots, \frac{1}{a_n}, \cdots\)
(5) \(\log a_1, \log a_2, \cdots, \log a_n, \cdots\)