MATH10560 Midterm: Math10560Practice Exam3Sp12Sol
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Solutions to practice exam 3, math 10560: find. Xn=1 (the series is geometric with a = 4. 5 . : discuss the convergence of the series. It"s an alternating series with bn = 1/ n. We have (i) the sequence {bn} n=2 is decreasing since n + 1 > n and thus bn+1 = 1/ n + 1 < 1/ n = bn for all n 2. (ii) limn bn = limn 1/ n = 0. N series converges by the alternating series test. Xn=2 diverges since it"s a p series and p = 1. 2 < 1: use comparison tests to determine which one of the following series is divergent. 2 + 1 n converges by comparison with. 1 n2 , a p-series with p = 2 > 1. 1 n converges by comparison with diverges by limit comparison with n2 + 8 n2 1 n3 + 100. 7(cid:18) 5 converges since it is a geometric series with |r| =
