Question

Consider the series ∑n=1 ∞ an where an=(5n+5)^(9n+1)/ 12^n In this problem you must attempt to...

Consider the series ∑n=1 ∞ an where

an=(5n+5)^(9n+1)/ 12^n

In this problem you must attempt to use the Ratio Test to decide whether the series converges.

Compute

L= lim n→∞ ∣∣∣an+1/an∣∣

Enter the numerical value of the limit L if it converges, INF if the limit for L diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity.
L=

Which of the following statements is true?
A. The Ratio Test says that the series converges absolutely.
B. The Ratio Test says that the series diverges.
C. The Ratio Test says that the series converges conditionally.
D. The Ratio Test is inconclusive, but the series converges absolutely by another test or tests.
E. The Ratio Test is inconclusive, but the series diverges by another test or tests.
F. The Ratio Test is inconclusive, but the series converges conditionally by another test or tests.
Enter the letter for your choice here: ?

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Determine whether the series Summation from n equals 0 to infinity e Superscript negative 5 n∑n=0∞e^−5n...
Determine whether the series Summation from n equals 0 to infinity e Superscript negative 5 n∑n=0∞e^−5n converges or diverges. If it​ converges, find its sum. Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice. A.The series converges because ModifyingBelow lim With n right arrow infinitylimn→∞ e Superscript negative 5 ne−5nequals=0. The sum of the series is nothing. ​(Type an exact​ answer.) B.The series diverges because it is a geometric series with StartAbsoluteValue r...
Determine if the series converges conditionally, converges absolutely, or diverges. /sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4) /sum(n=1 to...
Determine if the series converges conditionally, converges absolutely, or diverges. /sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4) /sum(n=1 to infinity) sin(4n)/4^n
Find a general term (as a function of the variable n) for the sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}. Find a...
Find a general term (as a function of the variable n) for the sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}. Find a general term (as a function of the variable n) for the sequence {?1,?2,?3,?4,…}={4/5,16/25,64/125,256/625,…} an= Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. (If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it diverges without being infinity or negative infinity, state your answer...
Test the series for convergence or divergence. ∞ (−1)n 8n − 5 9n + 5 n...
Test the series for convergence or divergence. ∞ (−1)n 8n − 5 9n + 5 n = 1 Step 1 To decide whether ∞ (−1)n 8n − 5 9n + 5 n = 1 converges, we must find lim n → ∞ 8n − 5 9n + 5 . The highest power of n in the fraction is 1    1 . Step 2 Dividing numerator and denominator by n gives us lim n → ∞ 8n − 5 9n +...
Use the ratio test to determine whether∑n=12∞n2+55n converges or diverges. (a) Find the ratio of successive...
Use the ratio test to determine whether∑n=12∞n2+55n converges or diverges. (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n≥12, 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∣∣∣ =   (c) By the ratio test, does the series converge, diverge, or is the test inconclusive?
Use the RATIO test to determine whether the series is convergent or divergent. a) sigma from...
Use the RATIO test to determine whether the series is convergent or divergent. a) sigma from n=1 to infinity of (1/n!) b) sigma from n=1 to infinity of (2n)!/(3n) Use the ROOT test to determine whether the series converges or diverges. a) sigma from n=1 to infinity of    (tan-1(n))-n b) sigma from n=1 to infinity of ((-2n)/(n+1))5n For each series, use and state any appropriate tests to decide if it converges or diverges. Be sure to verify all necessary...
(1 point) The three series ∑An, ∑Bn, and ∑Cn have terms An=1/n^8,Bn=1/n^5,Cn=1/n. Use the Limit Comparison...
(1 point) The three series ∑An, ∑Bn, and ∑Cn have terms An=1/n^8,Bn=1/n^5,Cn=1/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,...
1. Test the series below for convergence using the Root Test. ∞∑n=1 (4n/10n+1)^n The limit of...
1. Test the series below for convergence using the Root Test. ∞∑n=1 (4n/10n+1)^n The limit of the root test simplifies to lim n→∞ |f(n)| where f(n)= The limit is:     Based on this, the series Diverges Converges 2. We want to use the Alternating Series Test to determine if the series: ∞∑k=4 (−1)^k+2 k^2/√k^5+3 converges or diverges. We can conclude that: The Alternating Series Test does not apply because the terms of the series do not alternate. The Alternating Series Test...
1. To test the series ∞∑k=1 1/5√k^3 for convergence, you can use the P-test. (You could...
1. To test the series ∞∑k=1 1/5√k^3 for convergence, you can use the P-test. (You could also use the Integral Test, as is the case with all series of this type.) According to the P-test: ∞∑k=1 1/5√k^3 converges the P-test does not apply to ∞∑k=1 1/5√k^3 ∞∑k=1 1/5√k^3 diverges Now compute s4, the partial sum consisting of the first 4 terms of ∞∑k=1 1 /5√k^3: s4= 2. Test the series below for convergence using the Ratio Test. ∞∑n=1 n^5 /1.2^n...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT