Explain why you think the series n=1 converges to a finite number n+1 or diverges. If the series converges to a finite number, illustrate the problem

Q: What is the sum of the series corresponding to sequence: 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9,…

A: We have to find sum of the series:

Q: could you show how it converges via the geometric series?

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Q: 6. Tell whether the series whose nth term is given below converges absolutely, condition- ally, or…

A: Please post the multiple parts separately. Here I answered 1st question as per our policy.

Q: 2. ク

A: Convergence of the seriese

Q: 1. Firstly, we need to model this real-world situation with infinite series. Since the pendulum…

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Q: a1=1 , an+1=4-an , n is greater than or equal to 1 is the sequence convergent or divergent?  what if…

A: Given that a1=1 and an+1=4-an, n≥1 Write down the first few terms of the sequence: a1=1, Substitute…

Q: Write the first five terms of an infinite geometric series that converges to 2.

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Q: Tom has taken out a loan for college. He started paying off the loan with a first payment of $200.…

A: From given data the first payment of Tom = $200 The second payment is 1.2 times of first payment,…

Q: If you use the Alternating Series Test to help determine whether this series:

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Q: Create your own example of a convergent series for which you use the basic comparison test. Make…

A: To Do: Create an example of a convergent series and use the basic comparison test. And give a proper…

Q: State the first 4 terms of each sequence, then explain why each series is convergent, divergent, or…

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Q: If E-ja, is a convergent series of nonnegative numbers, can anything be said about Ea,/n)? Explain.…

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Q: Give an example of a convergent infinite series whose sum equals 2/11 . Explain how you know that…

A: To find the series which is convergent and whose sum is 211

Q: An alternating series is one whose terms alternate between even and odd.

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Q: n Question: Decide whether the series Σ converges or diverges. 1+n n=158 Explain your answer.

A: We have ∑n=158∞n1+n The necessary condition for positive term series  ∑un   is convergent if…

Q: 28

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Q: 1. Consider the following parameter values for the Lorenz equations: 0 = 10 r = r. = 470/19 = 24.74…

A: Lorentz equation is represented by x1.=σx2-x1x2.=rx1-x2-x1x3x3.=-bx3-x1x2…

Q: ) Pick your favourite real power series o a,r". Show that for this series, the equivalence 00 Σ anx"…

A: c) Take an=1n!. Then the series ∑n=0∞anxn=∑n=0∞xnn! and ∑n=1∞nanxn-1=∑n=1∞xn-1n-1!. To show that it…

Q: (-1)"-1 3n4 n=1

A: Given series, ∑n=1∞-1n-13n4 a) To find the convergence of the series.

Q: Astudent argues that (-1)" /n is an alternating series and therefore converges. Is the student…

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Q: A series converges to a sum of 13. The first term has a value of 3. Algebraically determine the…

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Q: Give the sequence an = 3n/5n From what I can tell the sequence converges but what is the value?

A: Sum =a/(1-r)  a is the first term r is the common ratio.

Q: How can you proof that this series is Converges?

A: We have a series ∑x=1∞cx2 We can use the integral test for convergence. It says that ∑x=1∞ax…