Mathematics > QUESTIONS & ANSWERS > Pennsylvania State University MATH 141-Written Homework 10. Solutions. Winter 2023. (All)

Pennsylvania State University MATH 141-Written Homework 10. Solutions. Winter 2023.

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Math 141 Written Homework 10 Page 1 of 4 Question 1 Determine whether each series converges or diverges. Be sure to name the test used and the key details. (a) 1 Xn =1 4n+1 5n (if this series con... verges, find its sum) 1 Xn =1 (n!)2 (2n)! (c) 1 Xn =1 3n + 2 5n + 3 (d) 1 Xn =1 35nn + 2 + 3 n Math 141 Written Homework 10 Page 2 of 4 (e) 1 Xn =1 102n+5n! (2n)! (f) 1 Xn =1 n! nn Math 141 Written Homework 10 Page 3 of 4 Question 2 Use the Alternating Series Estimation Theorem to find the minimum number of terms of the infinite series 1 X n =1 (-1)n n3 we need to add to approximate the sum of the series with jerrorj ≤ :008. Question 3 Captain Picard and the rest of the crew of the Rocinante are defending their position on Tatooine against the evil robotic Cylon invaders. Each day of the battle, 1500 Cylons arrive at dawn, and throughout each day the crew is able to eliminate 60% of the Cylons on the battlefield. (a) Let Cn be the number of Cylons on the planet at the end of the day on the nth day of the battle. Find C1; C2, and C3. Math 141 Written Homework 10 Page 4 of 4 (b) Find an explicit, closed-form formula for the number of Cylons at the end of the day on the nth day of the battle. (Explicit means we write Cn as a function of n alone as opposed to a recursive formula where Cn is written in terms of Cn-1. By closed-form, we mean a formula without shorthand such as sigma notation or + · · · +.) (c) In the long run, how many Cylons will be on the planet after a day of battle? (d) If instead the Cylons want to maintain a minimum force of 5000 soldiers, how many should they send each day? [Show More]

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