4 Answers: A, C, E, and F
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Explanation:
Choice A is true assuming we have [tex]a_n = (-1)^n*b_n[/tex]
In this case, [tex]a_n = (-1)^n*\frac{1}{\sqrt{n}}[/tex] and [tex]b_n = \frac{1}{\sqrt{n}}[/tex]
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Choice B is false. See choice A above.
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Choice C is true. The sequence [tex]\{b_n\}[/tex] is decreasing. As n gets larger, [tex]b_n[/tex] gets smaller. This is because the denominator is growing larger with the numerator held constant.
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Choice D is false. This contradicts choice C.
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Choice E is true since the denominator is growing forever
This is similar to [tex]\displaystyle \lim_{n \to \infty} \frac{1}{n} = 0[/tex]
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Choice F is true due to choices C and E being true.
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Choice G is false because it contradicts choice F.
