Explanation Result used: Consider the series ∑ a k with non-negative terms and r = lim k → ∞ | a k + 1 a k | . (i) If 0 ≤ r < 1 , then the series converges. (ii) If r > 1 ( including r = ∞ ) , then the series diverges. (iii) If r = 1 , then the test is inconclusive. Calculation: The given series ∑ k = 1 ∞ a k = ∑ k = 1 ∞ 2 k k ! . Here, the n th term is, a k = 2 k k ! . Thus, the ( n + 1 ) th term is, a k + 1 = 2 k + 1 ( k + 1 ) ! . Obtain the limit of | a k + 1 a k |

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ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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Chapter 8.5, Problem 10E

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Whether the series converges or not using the Ratio Test.

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Chapter 8 Solutions

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Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

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Whether the series converges or not using the Ratio Test.

Solution Summary: The author evaluates whether the series converges or not using the Ratio Test.

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Whether the series converges or not using the Ratio Test.

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