Proble m2. Determine, using compari sontests, if the following series converge or diverge. (2) [must use LCT]

Q: In the given equation as follows, use the Direct Comparison Test to determine the convergence or…

A: Given series is  ∑n=1∞1nn2+1 where an=1nn2+1

Q: In the given equation as follows , use the Ratio Test to determine the convergence or divergence of…

A: given,        ∑n=1∞5n!

Q: Q1 (- Use the comparison test to verify that the following series converges: 1 n =17+n6

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Q: Use the test of your choice to determine whether the following series converge.

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Q: In the given question as follows, use the Direct Comparison Test to determine the convergence or…

A: Consider the series ∑n=1∞sin2nn3

Q: Given the series: 1. k + 2 does this series converge or diverge? O converges Hiverge

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Q: Q\ Choose an appropriated series to compare with the series In(n) n3/2 n=1 and to guarantee it is…

A: Given series is ∑n=1∞un where  un=lognn32=lognnn Let us consider a series ∑n=1∞vn where vn=1n. Now,…

Q: Which of the following series converge, and which diverge? Give reasons for your answers. en 1 + e2n

A: To find whether the given series converges or diverges.

Q: sin (n) 2n=1 S 00 in: 5n

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Q: O Detemine the given series converges or diverges

A: a)  the given series is ∑n=1∞-1ncos1n     nth term of given series is an=-1ncos1n

Q: state whether the series converges or diverges

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Q: Use the comparison test to determine whether the following series converge. 2(n + 1)

A: Here, an=12(n+1) and 12(n+1)≈1n. So, let bn=1n. Now,…

Q: In the eqation given as follows , use the Ratio Test to determine the convergence or divergence of…

A: Given, ∑n=0∞2nn+2! To find the given series ids convergent or divergent.

Q: Use the test of your choice to determine whether the following series converge.

A: Given: ∑k=1∞ak=∑k=1∞k8k11+3 We have to determine whether the ∑k=1∞akseries converges.

Q: 1 Use the comparison test to determine whether the series converges or diverges. (3n + 1)15 n=1

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Q: If 14 the Series Converges and is approximated with Ss, would the approximation be an overstatem ent…

A: We will first expand the series

Q: Determine whether the series converges or diverges n=D1

A: Ratio test: The series ∑n=1∞an converges if L=limn→∞an+1an<1 and diverges if  L=limn→∞an+1an>1…

Q: Use the comparison test to verify that the following series converges: 1 Σ n =15+n4

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Q: In the root test if p>1 than the series is diverges O True false

A: In this question, we need to find whether the given statement is true or false.

Q: In  the given question as follows , verify that the Ratio Test is inconclusive for the p-series:-…

A: To verify the ratio test is inconclusive for the p-series:- ∑n =1∞1n3/2 To apply the ratio test  Let…

Q: Use an appropriate test to determine whether the following series converges. 4 Σ 3 k =1 vk

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Q: Use an appropriate test to determine whether the following series converges. 00 12 Σ 4. k=1 k

A: Definition: ∑k=1∞12k5=12∑k=1∞1k5=12∑k=1∞1(k)52 here p=52>1 this p is greater than 1 so using…

Q: Use an appropriate test to determine whether the following series converges. 7 Σ 3 k =1 VK

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Q: Use the test of your choice to determine whether the following series converge.

A: The given series is ∑k=1∞2kek-1  Applying Ratio Test to the above series.…

Q: Determine whether the series converges or diverges.

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Q: state whether the series converges or diverges

A: Apply ratio test and check weather series is convergent or divergent.

Q: In  the given question as solows , verify that the Ratio Test is inconclusive for the p-series:- see…

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Q: Use the test of your choice to determine whether the following series converge.

A: Ratio test: For the series ∑ak, limk→∞ak+1ak=L If L > 1, series is divergent. If L < 1, series…

Q: Employ a suitable comparison test to decide if the following series converge or Inn diverge (b) Σ…

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Q: In  the given question as folows , find the interval of convergence of the power series, where c…

A: Given series is  ∑n=0∞xkn=∑n=0∞xnkn where an=1kn.

Q: In the the question as attached here  find the radius of convergence of the power series:-

A: Here given series S=∑n=1∞4xnn2orS=∑n=1∞4nx nn2 Compare with ∑n=1∞anxn ⇒an=4nn2

Q: In  the given question as folows  determine the convergence or divergence of the series and identify…

A: Given: ∑n=1∞ 3nn2  To determine: The convergence or divergence of the series.

Q: Q1) Which of the series converge, and which diverge? Give reasons for your answers. In(n2) 1) Ln=2…

A: We will check the series that the series will  converge or diverge. We will solve the series using…

Q: `In In (1 - + n=1

A: The given series converges by Limit Comparison Test.

Q: If aN is the nth digit in the decimal expression of 1/3, is the series convergent or divergent?…

A: According to the given information, An is the nth digit in the decimal expression. So, for the…

Q: 00 n! WI

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Q: By using a suitable test determine whether the following series converges or diverges, give a reason…

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Q: Determine whether the following series converge.

A: Given: S=∑k=0∞-15k for evaluating given summation, first we expand given summation so,…

Q: 3n2 + 2n Σ n3 + n² + 1 n=1

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Q: Use the ratio test to determine the convergence of the series n! n=1 en?

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Q: By using a suitable test determine whether the following series converges or diverges, give a reason…

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Q: 6 Use the Ratio Test to determine whether the following series converges. (a) (b)

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Q: Apply the Ratio Test to determine convergence or divergence of the given series, or state that the…

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Q: Which of the series converge absolutely, which converge conditionally, and which diverge? Give…

A: Given that : The series ∑n = 1∞ 1n .

Q: Use an appropriate test to determine whether the following series converges. 00 Σ 4 k = 1 V

A: Explanation of the answer is as follows

Q: 2k+5 ニ k=1

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Q: Use the test of your choice to determine whether the following series converge.

A: Given: ∑k=1∞ 15k-1 To determine: Given series is convergent or divergent.

Q: Use the ratio test to determine if the following series converges or diverges. 6" Σ n! n=1

A: Given ∑n=1∞6nn!

Q: 1+ 4" 1+ 3" n=1

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