Question

How do you do this question?

Answer 1

4 Answers: A, C, E, and F

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Explanation:

Choice A is true assuming we have $a_n = (-1)^n*b_n$

In this case, $a_n = (-1)^n*\frac{1}{\sqrt{n}}$ and $b_n = \frac{1}{\sqrt{n}}$

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Choice B is false. See choice A above.

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Choice C is true. The sequence $\{b_n\}$ is decreasing. As n gets larger, $b_n$ 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  $\displaystyle \lim_{n \to \infty} \frac{1}{n} = 0$

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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.