Test the series below for convergence using the Root Test.8nΣ(Зп + 5n=1The limit of the root test simplifies to lim f(n) wheref(n) =The limit is:(enter oo for infinity if needed)

Answered: Test the series below for convergence…

Test the series below for convergence using the Root Test. n 8n Зп + 5 n=1 The limit of the root test simplifies to lim n- 00 |f(n)| where f(n) The limit is: (enter oo for infinity if needed)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 49E

See similar textbooks

Related questions

Q: e Σ k=1 3.

A: The objective is to determine whether the series converges using any appropriate test ∑n=1∞ennn

Q: Consider the series an where n-1 (-4n + 9)" (-5n – 8)2n an = In this problem you must attempt to use…

Q: Test the series below for convergence using the Root Test. ( 2n +5 3n+3 The limit of the root test…

A: Root Test : For a series ∑f(n) , 1. if limn→∞f(n)1/n<1 then the series is convergent and 2. if…

Q: 3n -3n =4 an +1 lim n

Q: Test the series for convergence or divergence. Š (-1)" n = 1 Identify an- Evaluate the following…

A: an=

Q: Test the series for convergence or divergence. 00 (5n - 4) 7n + 4 Σ(-1)" n = 1 Evaluate the…

Q: Find the interval of convergence of the series (-10x)" Enter INF for o and MINF for -o. п! n=1 The…

Q: Test the series below for convergence using the Root Test. 8n 4n + 1 n=1 The limit of the root test…

Q: Test the series below for convergence using the Ratio Test. nº 0.8" n=1 The limit of the ratio test…

A: Ratio test:

Q: Find the radius and interval of convergence of the series (r– 3)" Σ 2" /n +2 n=1 Test the end points

Q: Test the series for convergence or divergence using the Alternating Series Test. 8 10 9 10 11…

A: Solution: The series is -27+48-69+810-1011+...

Q: 1 for convergence, you can use the P-test. (You could also use the Integral Test, as To test the…

Q: Test the series for convergence or divergence. Σ n² + 8 6 n- 1 O convergent divergent

Q: Test the series below for convergence using the Root Test. Σ(13) 3n+ 5 The limit of the root test…

Q: Test the series below for convergence using the Root Test. 10n 5n + 4 n=1 The limit of the root test…

Q: Test the series below for convergence using the Root Test. 2n +2 Зп + 3 n=1 The limit of the root…

Q: Test the series for convergence or divergence. n+5 Σ n=1 n³-1 Show all work using the limit…

Q: Test the series below for convergence using the Root Test. 7n Зп + 3 n=1 The limit of the root test…

A: Given query is to find that Series is converging or diverging.

Q: Apply root test to the series n2 Eelan n n=1 The result is in the options given by (C, l) means the…

Q: (-1)*** n! 1.8-15... (7n t1) n+1 lim an+l

A: we have to test whether given series is convergent or divergent

Q: 00 k k 2. Σ (- 1)- k+1 k=0

Q: To test this series for convergence 67 4 n=1 You could use the Limit Comparison Test, comparing it…

Q: 3. Find the interval of convergence of the given series. Show your work! (x- 7)" 27 (n2 + 1) n=0

A: Explanation of the answer is as follows

Q: Use the root test to determine if the following series converges or diverges. 00 Σ n=1 (2+ (1/n))³n…

A: To find : The series is divergent or convergent .

Q: Determine whether the series converges or diverges. There may be more than one correct way to…

Q: 1). Apply the ratio test to the series. ∞ n! 6n3 n=1 Find the limit lim n→∞ an+1 an .…

A: Concept: Ratio Test: (1): If limn→∞an+1an=L<1 , then ∑n=1∞an is convergent (2): If…

Q: 2. Determine whether or not the series converges. State clearly the test you use, and show all…

A: We have to check the convergence

Q: Use the Ratio Test to determine the convergence or divergence of the series. 2n n = 1 an + 1 lim an…

Q: 2"-n n-12 '(-5)" n=1

A: NOTE: Refresh your page if you can't see any equations. . the sequence is

Q: Test the series below for convergence using the Root Tes 2n 7n +4 TL The limit of the root test…

Q: k! Σ 4k k=0 10

Q: To test this series for convergence n4 + 7 You could use the Limit Comparison Test, comparing it to…

A: We are going to solve

Q: Test the series below for convergence using the Ratio Test. 57 n! n=1 The limit of the ratio test…

Q: Test the series below for convergence using the Root Test. 2n бп + 3 n=1 The limit of the root test…

Q: n2 8. converges or diverges A +2 Use the Limit Comparison Test to determine whether the series n=1

A: The given series is ∑n=1∞n2n4+2. We have to find whether the series in convergent or divergent by…

Q: Test the series for convergence or divergence. n8 + n4 + 1 n-1 converges diverges

Q: Σ 00 6n To test for convergence you could use the limit comparison test and compare it with a n=1…

Q: for convergence, you can use the P-test. (You could also use the Integral k2 To test the series…

Q: Test the series for convergence or divergence using the Alternating Series Test. (-1)" - 1 Σ 4 + 7n…

A: Questions from alternating series.

Q: 2k converges or Determine if the series diverges. Explain 3k-1 k=1

Q: Consider the series > an where n=1 (-4n + 7)2n an = (-2n – 9)2n In this problem you must attempt to…

Q: To test this series for convergence п + 7 n=1 V 1 where p= You could use the Limit Comparison Test,…

Q: Determine the convergence or divergence of the series. (If you need to use co or -co, enter INFINITY…

Q: V** Use the Ratio Test to determine whether the series is convergent or divergent. * n300300" Σ n! n…

Q: Use the Ratio Test to determine whether the series is converge Σ (-6)" (2n + 1)! n = 0 Identify an.…

Q: . Use the Root Test to determine if the series (-1)" 2/n en? (2n² – 1)"¯ CONVERGES n=1 converges or…

Q: est the convergence or divergence of the series by limit comparsion k(k+3) 1 Zk=1 (2k+3)17' 4k2-2k+6…

Q: 3. Show that the power series (a)-(c) have the same radius of convergence. Then show that (a)…

Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

A: In root test, for an infinite series ∑n=1∞an the value for L=limn→∞ann is calculated. If L<1 than…

Question

Test the series below for convergence using the Root Test.
8n
Σ(
Зп + 5
n=1
The limit of the root test simplifies to lim f(n) where
f(n) =
The limit is:
(enter oo for infinity if needed)

Expert Solution

Step 1

Given: $\sum_{n = 1}^{\infty} {(\frac{8 n}{3 n + 5})}^{n}$

Step 2

Explanation:

Let $f (n) = {(\frac{8 n}{3 n + 5})}^{n}$

Root Test:

$L = \lim_{n \to \infty} |{(a_{n})}^{\frac{1}{n}}| = \lim_{n \to \infty} |{(a_{n})}^{\frac{1}{n}}| = \lim_{n \to \infty} |{(\frac{8 n}{3 n + 5})}^{\frac{n}{n}}| = \lim_{n \to \infty} |(\frac{8 n}{3 n + 5})| = \lim_{n \to \infty} |(\frac{8}{3 + \frac{5}{n}})| = \frac{8}{3} > 1$

So, given series are convergent series

The limit is: $\frac{8}{3}$

Step by step

Solved in 3 steps

Knowledge Booster

$Power Series$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN: