Question 1
For what values of x does the series
![](data:image/png;base64, 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)
n converge?
◦ on the interval (-∞, -1]
◦ for all x ≠ 0
◦ for x = 2 only
◦ on the intervals (-∞, -1] and [1, ∞)
◦ on the interval [1, ∞)
Question 2
For what values of x does the series
![](data:image/png;base64, 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)
converge?
◦ on the interval [-1, 1]
◦ on the intervals (-∞, -1] and [1, ∞)
◦ on the interval (-1, 1)
◦ on the intervals (-∞, -1) and (1, ∞)
◦ on the interval [1, ∞)