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Which of the Following Three Tests Will Establish That the Series

Question 125

Multiple Choice

Which of the following three tests will establish that the series n=1n2n5+1\sum _ { n = 1 } ^ { \infty } \frac { n } { \sqrt { 2 n ^ { 5 } + 1 } } converges?
1) Comparison Test with n=1n5/2\sum _ { n = 1 } ^ { \infty } n ^ { - 5 / 2 }
2) Comparison Test with n=1n3/2\sum _ { n = 1 } ^ { \infty } n ^ { - 3 / 2 }
3) Comparison Test with n=1n1/2\sum _ { n = 1 } ^ { \infty } n ^ { - 1 / 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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