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
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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.
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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?
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