Consider the following series. s (-1)" n = 2 In(3n) Test the series for convergence or divergence using the Alternating Series Test. Identify b, Evaluate the following limit. lim b Since lim b, in O and bn + 1 b for all n, the series converges

Calculus: Early Transcendentals
8th Edition
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the following series.
00
(-1)"
In(3n)
n = 2
Test the series for convergence or divergence using the Alternating Series Test.
Identify bn
Evaluate the following limit.
lim bn
Since lim b =
0 and b,
A b for all n, the series converges
n+ 1
Test the series b, for convergence or divergence using an appropriate Comparison Test.
The series converges by the Limit Comparison Test with a convergent p-series.
O The series diverges by the Limit Comparison Test with a divergent geometric series.
O The series converges by the Direct Comparison Test. Each term is less than that of a divergent geometric series.
The series diverges by the Direct Comparison Test. Each term is greater than that of a comparable harmonic series.
Determine whether the given alternating series is absolutely convergent, conditionally convergent, or divergent.
absolutely convergent
conditionally convergent
O divergent
Transcribed Image Text:Consider the following series. 00 (-1)" In(3n) n = 2 Test the series for convergence or divergence using the Alternating Series Test. Identify bn Evaluate the following limit. lim bn Since lim b = 0 and b, A b for all n, the series converges n+ 1 Test the series b, for convergence or divergence using an appropriate Comparison Test. The series converges by the Limit Comparison Test with a convergent p-series. O The series diverges by the Limit Comparison Test with a divergent geometric series. O The series converges by the Direct Comparison Test. Each term is less than that of a divergent geometric series. The series diverges by the Direct Comparison Test. Each term is greater than that of a comparable harmonic series. Determine whether the given alternating series is absolutely convergent, conditionally convergent, or divergent. absolutely convergent conditionally convergent O divergent
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