MAT-1120 Midterm: MATH 1120 App State Spring2014 Test3 answer key
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5n + 1 is positive, decreasing, and limits to 0. Thus this is a convergent alternating series (by the alternating series test). However, if we consider the absolute value of our terms, we get compared with the harmonic series (either directly or using the limit comparison test): lim n . [note: both series are non-negative so the limit comparison test does actually apply. ] This means that our series converges, but does not converge absolutely. The nth-term test doesn"t say anything since the terms limit to 0. Xn=1 applied to nd that the limit of the ratio is 1). 5n + 1 diverges (but comparison is easier). The ratio test tells us nothing here (we get that (b) Since the limit of the ratio of terms is less than 1, we get (absolute) convergence. ( 2)(n + 1) This series is non-negative and can be compared with the harmonic series.
