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(1 point) What can you say about the series an in each of the following cases using the Ratio Test? Answer "Convergent," "Divergent," or "Inconclusive." an+1 1. lim T-100 an ? ? ? V 2. lim TL 100 3. lim 1 00 an+1 an an+1 an = 0.2 = 1 = 5

(1 point) What can you say about the series an in each of the following cases using the Ratio Test? Answer "Convergent," "Divergent," or "Inconclusive." an+1 1. lim T-100 an ? ? ? V 2. lim TL 100 3. lim 1 00 an+1 an an+1 an = 0.2 = 1 = 5

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Exercise: Applying the Ratio Test to Determine Convergence** **Problem Description:** What can you say about the series \( \sum a_n \) in each of the following cases using the Ratio Test? Answer "Convergent," "Divergent," or "Inconclusive." 1. \( \lim_{{n \to \infty}} \left| \frac{{a_{n+1}}}{a_n} \right| = 0.2 \) 2. \( \lim_{{n \to \infty}} \left| \frac{{a_{n+1}}}{a_n} \right| = 1 \) 3. \( \lim_{{n \to \infty}} \left| \frac{{a_{n+1}}}{a_n} \right| = 5 \) **Instructions:** - For each case, select the appropriate convergence status: Convergent, Divergent, or Inconclusive. Use the Ratio Test to justify your answer.
Transcribed Image Text:**Exercise: Applying the Ratio Test to Determine Convergence** **Problem Description:** What can you say about the series \( \sum a_n \) in each of the following cases using the Ratio Test? Answer "Convergent," "Divergent," or "Inconclusive." 1. \( \lim_{{n \to \infty}} \left| \frac{{a_{n+1}}}{a_n} \right| = 0.2 \) 2. \( \lim_{{n \to \infty}} \left| \frac{{a_{n+1}}}{a_n} \right| = 1 \) 3. \( \lim_{{n \to \infty}} \left| \frac{{a_{n+1}}}{a_n} \right| = 5 \) **Instructions:** - For each case, select the appropriate convergence status: Convergent, Divergent, or Inconclusive. Use the Ratio Test to justify your answer.
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