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Math 1320 Lab 5 Name: Unid: 1. Determine if the following series converge or not. If so, do they converge absolutely? ∞ X sin(πn) (a) n1/10000 n=1 (b) ∞ X cos(πn)7 n=1 n 2. Use any method to determine whether the following series converges. ∞ X n− ln n n=1 Page 2 3. Radius of convergence. Give an example of power series with the following radius of convergence respectively: (a) R = 0; (b) R = 2; (c) R = ∞. Justify your answers. Page 3 4. A ball is thrown horizontally from a height of 30 feet with initial velocity in the xdirection of 10 feet per second. Each time it bounces, it reaches a height equal to 84% of the height it reached on the previous bounce. Assuming the ball maintains a constant velocity in the x-direction, what is the total distance the ball travels in the vertical direction? Page 4