1001anbn converges and limn00 b,lem 5. Let {an} and {b,} each be a sequence of positive real numbers. You know that10k=1Your buddy Ron states that since the limit above is computed to be 1001, the series diverges by the ratio test. State whether Ron is correct or incorrect and explain why or why not.

Answered: Image /qna-images/answer/02f36478-a1a0-4700-a797-ed2c209dda2a.jpg

Answered: 1001 an bn converges and lim no b, lem…

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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Similar questions

00 If 8¹ is convergent, does it follow that the following series are convergent? n n=0 Choose the correct statements. n=0 OC (-6) is convergent. n=0 n=0 (-8)" is convergent. n=0 (-8)" isn't necessarily convergent. (-)" isn't necessarily convergent.
Find if the series converges or diverges.
Suppose ∑ an & ∑ bn are series with only positive terms and ∑ bn is known to be convergent. If an>bn for all n, what can you say about ∑ an? Why? *Choose the correct multiple choice and explain why*
The three series An, Bn, and Cn have terms 1 1 1 a C, = An B, n8 » n Use the Limit Comparison Test to compare the following series to any of the above series. For each of the series below, you must enter two letters. The first is the letter (A,B, or C) of the series above that it can be legally compared to with the Limit Comparison Test. The second is C if the given series converges, or D if it diverges. So for instance, if you believe the series converges and can be compared with series C above, you would enter CC; or if you believe it diverges and can be compared with series A, you would enter AD. 5n2 + 5n7 1. 4n8 + 7n3 – 4 n= 4n4 +n8 2. E 1496n12 + 7m4 + 5 n=1 5n5 + n2 – 5n - 3. 7n13 – 5n10 +8 n=1
Use the Ratio Test to find the real numbers x for which the series E (x-1)* converges. (Use symbolic notation and fractions where needed. Give your answer as intervals in the form (*,*). Use the symbol oo for infinity, U for combining intervals, and an appropriate type of parenthesis "(" ")", "[" or "]" depending on whether the interval is open or closed.)
For each set of conditions below, give an example of sequences/series that satisfy the conditions (and show that they do), or explain why the sequence/series cannot exist. (a) A sequence {an} that is not monotonic, but converges to the limit 2021. (b) A series > a, that can be shown to converge using the Integral Test, but not the Ratio Test. 00 (c) Two different series > An and bn that converge to the same sum, and another series ) Cn that diverges, n=1 n=1 n=1 such that an < Cn < bn for all n.

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