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Math
CalculusCalculus10th Edition

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Chapter 9.3, Problem 24E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Chapter
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Problem 1E
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Problem 6E
Problem 7E
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Problem 9E
Problem 10E
Problem 11E
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Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
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Problem 31E
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Problem 33E
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Problem 37E
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Problem 44E
Problem 45E
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Problem 48E
Problem 49E
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Problem 66E
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Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Using the Integral Test In Exercises 23 and 24, use the Integral Test to determine be convergence or divergence of the series, where k is a positive integer.

∑ n = 1 ∞ n k − 1 n k + c

To determine

To calculate: The convergence or divergence of the given series ∑n=1∞nke−n by using an Integral test.

Explanation

Given: The series ∑n=1∞nke−n

Calculation:

Here, the given series is ∑n=1∞nke−n. Now, let the function f(x)=xkex as k is positive. Hence, the function f(x)=xkex) is positive and continuous for all x≥1 and the derivative of f(x) is, f′(x)=xk−1(k−x)ex, which is decreasing, that is, f'(x)<0 for x>1. This proves that f(x) fulfills all the conditions of an integral test

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Chapter 9.3,
Problem 23E
Chapter 9.3,
Problem 25E
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P-109RECh-9 P-110RECh-9 P-1PSCh-9 P-2PSCh-9 P-3PSCh-9 P-4PSCh-9 P-5PSCh-9 P-6PSCh-9 P-7PSCh-9 P-8PSCh-9 P-9PSCh-9 P-10PSCh-9 P-11PSCh-9 P-12PSCh-9 P-13PSCh-9 P-14PSCh-9 P-15PSCh-9 P-16PS

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