Using the Ratio Test In Exercises 19–32, use the Ratio Test to determine the convergence or divergence of the infinite series. See Examples 3, 4, and 5.
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Calculus: An Applied Approach (MindTap Course List)
- Express the sums in Exercises 11–14 in sigma notation. The form of your answer will depend on your choice for the starting index. 11. 1 + 2 + 3 + 4 + 5 + 6 12. 1 + 4 + 9 + 16 13. 1/ 2 + 1 /4 + 1/ 8 + 1/ 16 14. 2 + 4 + 6 + 8 + 1arrow_forwardIn Exercises 33–38, use Theorem 9.11 to determine the convergence or divergence of the p-series.arrow_forwardUsing sigma notation, write the expression -8+ 8 – 8 + 8 – 8 + 8+... as an infinite series in two ways, one with the index starting at 0 and one with the index starting at 1. 00 (a) –8 + 8 – 8 + 8 – 8 + 8+. .= an, where an help (formulas) - n=0 (b) –8 + 8 – 8+ 8 – 8 + 8+...= > bn, where bn help (formulas) n=1arrow_forward
- In Exercises 13–16, match the sequence with the given nth term with its graph. [The graphs are labeled (a), (b), (c), and (d).]arrow_forwardReal Analysis II: Prove whether the series is convergent or divergent. Please follow example in other photoarrow_forwardCalculus 2 Question:Section 9.2: Infinite Series Determine whether the following geometric series is convergent or divergent.If it is convergent, find its sum. Show your work.arrow_forward
- Calculus 2 Is the series convergent or divergent? State the reason.arrow_forwardPAGE ONE JENCES AND SERIES: onvergent or divergent and, if convergen 23 an 20 ,n=1,2,3,...arrow_forwardSome applications of calculus use a mathematical structure called a power series. To find the interval of convergence of a power series, it is often necessary to solve an absolute value inequality. For Exercises 11–12, solve the absolute value inequality to find the interval of convergence. x + 1 11. < 1 2 < 1 12.arrow_forward
- Calculus 2 Question:Section 9.1: Infinite Sequences and Series Determine whether the following sequence converges or diverges. If it converges, find the limit. Show your work.arrow_forwardCalculus II state whether the series converges or diverges. Please provide work/explanation whyarrow_forwardPart II: Recursion (10 pt.) 7. Give the first six terms (including the initial terms) of the following recursively defined sequences: a. dį = 1 d2 = 1 dn = (dn-1)² + dn-2 for n > 3 b. e1 = 0 ez = 2 en = 5. en-1 - 2 · en-2 for n > 3arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage