EXAMPLE 1 Determine whether the series 3 7n² SOLUTION For large n the dominant term in the denominator is 7n², so we compare the given series with the series > 3/(7n²). Observe that 3 7n² + 2n +8 7n² because the left side has a bigger denominator. (In the notation of the Comparison Test, a, is the left side and b,, is the right side.) We know that 3 7n² + 2n +8 3 7n² + 2n +8 converges or diverges. n=1 n=1 is convergent because it's a constant times a p-series with p = | > 1. Therefore n=1 is ---Select---✓ by the Comparison Test.

EXAMPLE 1 Determine whether the series 3 7n² SOLUTION For large n the dominant term in the denominator is 7n², so we compare the given series with the series > 3/(7n²). Observe that 3 7n² + 2n +8 7n² because the left side has a bigger denominator. (In the notation of the Comparison Test, a, is the left side and b,, is the right side.) We know that 3 7n² + 2n +8 3 7n² + 2n +8 converges or diverges. n=1 n=1 is convergent because it's a constant times a p-series with p = | > 1. Therefore n=1 is ---Select---✓ by the Comparison Test.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter13: Sequences And Series

Section13.CR: Chapter Review

Problem 6CC

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