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Which of the Following Series Will, When Rearranged, Converge to Different

Question 119

Multiple Choice

Which of the following series will, when rearranged, converge to different values?
1) n=1n1\sum _ { n = 1 } ^ { \infty } n ^ { - 1 }
2) n=1(1) n1n1\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } n ^ { - 1 }
3) n=1(1) n1n2\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } n ^ { - 2 }


A) None
B) 1
C) 2
D) 3
E) 1, 2
F) 1, 3
G) 2, 3
H) 1, 2, 3

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