n + 9Use the ratio test to determine whethern!n=14converges or diverges.(a) Find the ratio of successive terms. Write youranswer as a fully simplified fraction. For n ≥ 14,an+1lim= limn→∞anN→∞(b) Evaluate the limit in the previous part. Enter ∞ as infinityand →∞ as -infinity. If the limit does not exist, enter DNE.an+1lim=N→∞ An(c) By the ratio test, does the series converge, diverge, or isthe test inconclusive? Choose

Answered: Image /qna-images/answer/7b29fd33-f500-4d96-9352-2d83e229fd37.jpg

Answered: ∞ Use the ratio test to determine…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 71E

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Similar questions

Find the limit if it exists of Anx1 as n approaches infinity, where A=[02120], and x1=[aa]
Use the ratio test to determine whether ∑n=6∞n2+66n∑n=6∞n2+66n converges or diverges.(a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n≥6n≥6, 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?
limit of the sequence lim h→∞ （1+2/h)^h
Let r > 0 be a positive real number. This problem will give a simple approach to limn→∞ rn. i. Explain briefly why an = rn can be written recursively as a0 = 1, an = r ⋅ an-1 for n > 0. ii. Using the technique of solving for the limit of a recursive sequence, find the possible limits of an if the sequence converges. iii. Show that an is monotone. (It may be increasing or decreasing, depending on r.) iv. Combine (ii) and (iii) to show limn→∞ rn converges to 0 for r < 1, converges to 1 for r = 1, and diverges to ∞ for r > 1.
Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. an=n/12n Select the correct choice below and, if necessary, fill in the answer box to complete the choice A) The sequence converges to lim n—>∞ an = ( ) B) The sequence diverges
Let r > 0 be a positive real number. This problem will give a simple approach to limn→∞ rn. i. Explain briefly why an = rn can be written recursively as a0 = 1, an = r ⋅ an-1 for n > 0. ii. Using Problem A and (i), solve for the possible limits of an if the sequence converges. iii. Show that an is monotone. (It may be increasing or decreasing, depending on r.) iv. Combine (ii) and (iii) to show limn→∞ rn converges to 0 for r < 1, converges to 1 for r = 1, and diverges to ∞ for r > 1.

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