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∞ (-1)" In(n) n=2 Consider the following convergent alternating series: S = know that 0 < ln(n) ≤ n for all n ≥ 2. (a) Is this series absolutely convergent? Justify your answer, and clearly state the nan the test you are using. (b) You may find it useful J Is it accurate to say that this series is conditionally convergent? Give a bri justification based on your answer to part (a). (c) ! Give an upper bound (rounded to 4 decimal places) on the error |R150| if we use t partial sum S150 to estimate S. Briefly justify your answer, and state the name of the theore you're using. (You do not need to compute S150).

∞ (-1)" In(n) n=2 Consider the following convergent alternating series: S = know that 0 < ln(n) ≤ n for all n ≥ 2. (a) Is this series absolutely convergent? Justify your answer, and clearly state the nan the test you are using. (b) You may find it useful J Is it accurate to say that this series is conditionally convergent? Give a bri justification based on your answer to part (a). (c) ! Give an upper bound (rounded to 4 decimal places) on the error |R150| if we use t partial sum S150 to estimate S. Briefly justify your answer, and state the name of the theore you're using. (You do not need to compute S150).

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.3: Geometric Sequences
Problem 98E
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∞ (−1)n In(n) n=2 You may Consider the following convergent alternating series: S = know that 0 < ln(n) ≤ n for all n ≥ 2. (a) Is this series absolutely convergent? Justify your answer, and clearly state the name the test you are using. (b) find it useful to J Is it accurate to say that this series is conditionally convergent? Give a brief justification based on your answer to part (a). (c)! Give an upper bound (rounded to 4 decimal places) on the error |R150| if we use the partial sum S150 to estimate S. Briefly justify your answer, and state the name of the theorem you're using. (You do not need to compute S150).
Transcribed Image Text:∞ (−1)n In(n) n=2 You may Consider the following convergent alternating series: S = know that 0 < ln(n) ≤ n for all n ≥ 2. (a) Is this series absolutely convergent? Justify your answer, and clearly state the name the test you are using. (b) find it useful to J Is it accurate to say that this series is conditionally convergent? Give a brief justification based on your answer to part (a). (c)! Give an upper bound (rounded to 4 decimal places) on the error |R150| if we use the partial sum S150 to estimate S. Briefly justify your answer, and state the name of the theorem you're using. (You do not need to compute S150).
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