Explanation Concept Used: Root Test: Let ∑ k = 1 ∞ a k be a series with nonzero terms. Let L = lim k → ∞ | a k | k = lim k → ∞ | a k | 1 k i. If L < 1 , then the series converges absolutely. ii. If L > 1 or L = ∞ , then the series diverges. iii. If L = 1 , the test does not provide any information. Given the power series ∑ k p e − k , we start by applying ratio test to find if this series is convergent or not. In this case ∑ k = 1 ∞ a k = ∑ k p e − k ⇒ a k = k p e − k Therefore, L = lim k → ∞ |

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 8.5, Problem 55PS

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To show: using root test the given series converges. ∑kpe−k .

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Chapter 8.5, Problem 54PS

Chapter 8.5, Problem 56PS

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Chapter 8 Solutions

Calculus

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using root test the given series converges. ∑ k p e − k .

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Chapter 8 Solutions