7. Determine the convergence/divergence of the seriesn=09. Determine the convergence/divergence of the series8. Determine the convergence/divergence of the series (√n² + 2n − n)n=1n!100n +n100k=17k³+k6k(3k)! + log4 k

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Answered: 7. Determine the convergence/divergence…

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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Use any method to determine whether the series converge. 1 (a) 2 k* + 9k + 1 k=1 This series (b) 2 (7 + k)/5 k=1 This series >
Consider the series San where n=1 (-1)"n n² + 2n + 5 In this problem you must attempt to use the Ratio Test to decide whether the series converges. Compute an = an+1 L = lim n-00 an Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, -INF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L = Which of the following statements is true? A. The Ratio Test says that the series converges absolutely. B. The Ratio Test says that the series diverges. C. The Ratio Test says that the series converges conditionally. D. The Ratio Test is inconclusive, but the series converges absolutely by another test or tests. E. The Ratio Test is inconclusive, but the series diverges by another test or tests. F. The Ratio Test is inconclusive, but the series converges conditionally by another test or tests. Enter the letter for your choice here:
8. (a) Determine whether each series converges or diverges and write a brief explanation. (-1)¹¹¹ ·n n=1n² +3n+1 n Σ n=1n² +3n+1 Σ0.4(1.2)" n=0
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7. Determine the convergence/divergence of the series > n=0 8. Determine the convergence/divergence of the series (√n² +2n − n) n=1 n! 100n +n100 9. Determine the convergence/divergence of the series > k=1 7k³+k6k (3k)! + log4 k