6n3 – 4n² + 16Use the limit comparison test to determine whetherconverges or diverges.7+ 3n4(a) Choose a seriesb, with terms of the form b, =1and apply the limit comparison test. Write your answer as a fully simplified fraction. Forn=16n> 16,anlimn→00 bn= limn007+ 3n(b) Evaluate the limit in the previous part. Enter as infinity and -∞ as -infinity. If the limit does not exist, enter DNE.anlim= 2n0o bn(c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive? Diverges

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Answered: 6n³ – 4n² + 16 Use the limit comparison…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 71E

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Use the ratio test to determine whether ∑n=21∞5n(2n)!∑n=21∞5n(2n)!x converges or diverges.(a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n≥21n≥21, limn→∞∣∣∣an+1an∣∣∣=limn→∞limn→∞|an+1an|=limn→∞ (b) Evaluate the limit in the previous part. Enter ∞∞ as infinity and −∞−∞ as -infinity. If the limit does not exist, enter DNE.limn→∞∣∣∣an+1an∣∣∣limn→∞|an+1an| = (c) By the ratio test, does the series converge, diverge, or is the test inconclusive?
Determine whether the sequence xn =√(5+3n+7n2)/(4n2-n+2), converges or diverges. If it converges, find the limit
∑n=1∞3⋅7⋅11⋯(4n−1)4⋅9⋅14⋯(5n−1).∑n=1∞3⋅7⋅11⋯(4n−1)4⋅9⋅14⋯(5n−1). Which test is the best test to use for this series? Let's try Ratio Test: Compute limn→∞∣∣∣an+1an∣∣∣=limn→∞|an+1an|= . (Note: Use INF for an infinite limit, DNE if the limit does not exist.) Since the limit is , the Ratio Test tells us .
For ∑ 1/(n - π) and ∑ (n - 1)/(n3 + 1), solve with either big Θ or with Limit Comparison.
4). For the sequence, determine if the divergence test applies and either state that lim n→∞ an does not exist or find lim n→∞ an. (If an answer does not exist, enter DNE.) an = (4n + 1)2n (5n2 + 1)n lim n→∞ an = The divergence test applies. The divergence test does not apply.
A ball is thrown upward to a height of h0 meters. After each bounce, the ball rebounds to a fraction r of its previous height. Let hn be the height after the nth bounce and let Sn be the total distance the ball has traveled at the moment ofthe nth bounce.a. Find the first four terms of the sequence {Sn}.b. Make a table of 20 terms of the sequence {Sn} and determine aplausible value for the limit of {Sn}. h0 = 20, r = 0.5
Evaluate the limit lim n→ ∞ √( 9n^4)+13n^3-5n-10 / -√( 25n^16)+5n^2-9n Also find the asymptotic value of above limit
Does the sequence an converge or diverge? Find the limit if the sequence is convergent. an=2+6n4/n4 + n4+4n3 does the sequence diverge? If the sequence converges. To what Iim n-->infinity an=?
The nth term of a sequence is represented by 2n4+25n2+32n−156n4+2n3−11n2−2n+17. What is the limit of the the nth term as x becomes increasingly large?
a) find sn , (b) evaluate lim n→+∞sn, then (c) conclude whether the infiniteseries is convergent or divergent.
Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive.∑n=1∞enn!ρ=limn→∞|an+1an|= (Enter 'inf' for ∞.) ∑n=1∞enn! is:A. convergentB. divergentC. The Ratio Test is inconclusive
4). Use the Ratio Test to determine whether ∞ n = 1an converges, where an is given. State if the ratio test is inconclusive.∞ n = 134n(n!)4(4n)!Identify an. Evaluate the following limit. lim n → ∞ an+1an Since lim n → ∞ an+1an 1, . please show step by step .

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