Consider the series67 +46n³-6n+8We will try to use the ratio test to determine whether this series converges.an+1(a) Enter an expression for the ratioan(b) Determine the limitan+1limn→∞ angiving the exact value数字where an represents the nth term in the series.

To use ratio test to determine whether the given series converges or diverges

Answered: Consider the series 6+4 6n³-6n+8 n= We…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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:
Use the Ratio Test to determine whether the series is convergent or divergent. 1 40 2(-1)0 - 1 30n3 n = 1 Identify a Evaluate the following limit. a n + 1 lim a Since lim 1, the series is divergent a
6. Let a be a real number. Consider the series where an = cos(na): 2n +1 n=0 (a) Is it possible to find an a > 0 such that the above series is both absolutely convergent and conditionally convergent? Briefly explain your reasoning. (b) Find all a > 0 such that the series diverges. (c) Find all a > 0 such that the series converges absolutely. (d) Find all a > 0 such that the series converges conditionally.
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Consider the series Σ(n+1)7²n+1 In this problem you must attempt to use the Ratio Test to decide whether the series converges. Compute L = lim n-00 an+1 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 = Motor in order 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:
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Consider the series 6+4 6n³-6n+8 n= We will try to use the ratio test to determine whether this series converges. (a) Enter an expression for the ratio (b) Determine the limit an+1 lim n→∞o an giving the exact value 数字 an+1 where an represents the nth term in the series. an