quiz06_s107_solns - Name: Math 1B Quiz 6 Solutions Section...

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Name: Math 1B Quiz 6 Solutions Section 107 October 13, 2009 1. (4 points) Test the series for convergence or divergence: X n =1 tan - 1 (1 /n ) n Use the Limit Comparison Test with the convergent p-series 1 n 3 / 2 . Calculate: lim n →∞ tan - 1 (1 /n ) n 1 n n = lim x →∞ tan - 1 (1 /x ) 1 x = lim x →∞ ( - 1 /x 2 ) 1 (1 /x ) 2 +1 ( - 1 /x 2 ) = 1 . Since the limit is strictly between 0 and (0 < 1 < ), the LCT applies. Therefore, since 1 n 3 / 2 converges, tan - 1 (1 /n ) n converges. 2. (4 points) Test the series to determine whether it diverges, converges conditionally, or converges absolutely. X n =1 ( - 1) n (3 1 /n 2 - 1) n Use the root test. Calculate:
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