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Math 3210-3 HW 25 Due Friday, November 30, 2007 Convergence Tests 1. Determine the values of p for which the series ∞ X 1 converges. n(log n)p n=2 2. Determine whether each series converges conditionally, converges absolutely, or diverges. Justify your answers. (a) ∞ X (−1)n log n n=1 (b) X (−2)n (c) n2 X (−3)n n! X 1 1 √ − (d) n n 3. Find an example to show that P the convergence of imply the convergence of (an bn ). 4. Show that the series P an and the convergence of 1 1 1 1 1 1 1 + − 3 + − 4 + ··· + − 2 3 22 5 2 7 2 diverges. Why doesn’t this contradict the alternating series test? 1− P bn do not necessarily