Convergence of the series sum k = 1 to ∞ (-1)^k * ((k + 1)/k) The series is (a) Carefully determine the convergence A. absolutely convergent B. conditionally convergent C. divergent (b) Carefully determine the convergence of the series sum k = 1 to ∞ ((-1)^k)/(3k) The series is A. absolutely convergent B. conditionally convergent C. divergent (c) Carefully determine the convergence of the series sum k = 1 to ∞ ((-1)^k)/(3^k) The series is A. absolutely convergent B. conditionally convergent C. divergent
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This series is alternating and the terms approach 0 as k approaches infinity. Show more…
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converges or diverges: this series
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(a) Check all of the following that are true for the series sum(n=1 to infinity) 3^n / (2^n - 1): A. This series converges. B. This series diverges. C. The integral test can be used to determine convergence of this series. D. The comparison test can be used to determine convergence 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 sum(n=1 to infinity) (n^3 - 3)cos(n*pi) / n^4: A. This series converges. B. This series diverges. C. The integral test can be used to determine convergence of this series. D. The comparison test can be used to determine convergence 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.
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