fall17mth143.practice2.4-ConvergenceTestsII.pdf

# Absolutely convergent conditionally convergent

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(incorrect) Correct Answers: C A D C D B 18. (1 point) (a) Check all of the following that are true for the series n = 1 6 n 2 n - 1 A. This series converges B. This series diverges C. The integral test can be used to determine conver- gence of this series. D. The comparison test can be used to determine con- vergence of this series. E. The limit comparison test can be used to determine convergence of this series. F. The ratio test can be used to determine convergence of this series. G. The alternating series test can be used to determine convergence of this series. (b) Check all of the following that are true for the series n = 1 ln ( 2 n )+ 6 n n 2 A. This series converges B. This series diverges C. The integral test can be used to determine conver- gence of this series. D. The comparison test can be used to determine con- vergence of this series. E. The limit comparison test can be used to determine convergence of this series. F. The ratio test can be used to determine convergence of this series. G. The alternating series test can be used to determine convergence of this series. Solution: SOLUTION (a) For this series, the terms in the series involve exponen- tials, so that the ratio test is a good choice to test convergence. If we’re careful we can find a comparison series that will work, and the limit comparison test will definitly work. The require- ments for the integral test are satisfied, but we can’t integrate the function f ( x ) = 6 x 2 x - 1 , so it’s not good to assess the convergence of the series. The alternating series test isn’t applicable, because
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