Answered: ∞ (2) Use the Limit Comparison Test to… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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can someone help me with this calculus question, thanks

In certain situations, the (Direct) Comparison Test has limited application
because comparing functions (in n) can be challenging. In such situations, you might try using the
Limit Comparison Test as stated below.
Theorem (The Limit Comparison Test). Suppose Σ
An
n=1
an and Σ bn are series with
n=1
positive terms. If lim = c where c is a finite number and c > 0, then either both
nxx bp
series converge or both diverge.
(2) Use the Limit Comparison Test to determine whether the series Σ cot
Σοκ (1)
is convergent.
n=1

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Select the FIRST correct reason why the given series diverges . A. Diverges because the terms don't have limit zero (nth Term Test for Divergence)B. Divergent geometric seriesC. Divergent p seriesD. Integral testE. Comparison with a divergent p seriesF. Cannot apply any test done so far in class
5. For this problem, you have to read and study the textbook pages 762-763 about The Limit Comparison Test: Suppose that an and bn are series with positive terms. n=1 n=1 If an lim n-0o bn = C where c is a finite number with c> 0, then either both series converge or both diverge. For the following problems, you must use the Limit Comparison Testr. No points will be given for solutions that do not use the Limit Comparison Test. (a) ks) Determine whether the series 5n10 + 2n + 1 Vn 4064 +1 n=1 converges or diverges by comparing with Σ 1 n 2022 n=1 You have to use the Limit Comparison Test to justify your answer. (b) rks) Determine whether the series cot n=1 converges or diverges. You have to use the Limit Comparison Test to justify your answer.
5. For this problem, you have to read and study the textbook pages 762- 763 about The Limit Comparison Test: Suppose that an and bn are series with positive terms. n=1 n=1 If an lim no b, where c is a finite number with e> 0, then either both series converge or both diverge. For the following problems, you must use the Limit Comparison Test. No points will be given for solutions that do not use the Limit Comparison Test. (a) Determine whether the series 5n 10 + 2n +1 n4064 +1 converges or diverges by comparing with n 2022 n=1 You have to use the Limit Comparison Test to justify your answer. (b) Determine whether the series Σο() cot n=1 converges or diverges. You have to use the Limit Comparison Test to justify your answer.
If gan converges and Σbn diverges, can anything be said about their term-by-term sum Σ(an + bn)? Give reasons for your answer.
In the given equation as follows, test for convergence or divergence, using each test at least once. Identify which test was used:- (a) nth-Term Test (b) Geometric Series Test(c) p-Series Test (d) T elescoping Series Test(e) Integral Test (f ) Direct Comparison Test(g) Limit Comparison Test see the equation as attached here.
Use the limit comparison test to determine whether the following seriesconverges or diverges
Let s suppose that you have a set oftime-series variables, and you want to model the relationshipbetween them. Read the situations given below and answer the questions. a ) Explain the statistical test if the linear combination (of time-series variables) is I(0). b) Which statistical test can be applied if all the series are integrated of the same order I/( 1).Justify your answer
Find 2x xp (if it converges)
Q. 3 Show that full range series is an extension of Half Rage.
"Find the divergance or convergance of each non highlighted series
2n+1 3. Test the convergence of Ln=1 n3+1 by limit comparison test.
Entered DIV 0.25 At least one of the answers above is NOT correct. (a) The series Σ(An). Div n=1 Answer Preview (b) The sequence {An}. DIV Given: 3n An = 12n + 13 For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, -INF if it diverges to minus infinity, or DIV otherwise. 1 4

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