Suppose ak > 0 for all k, and ∑ ak converges.                                                   k=1 Answer the following questions and explain your reasoning.               ∞        a. Must ∑−3an always converge?               n=1               ∞ b. Must ∑ 1/an always converge?              n=1              ∞ c. Must ∑(an )^3 always

Q: did I do this right? 8.6.4.   Determine the radius and interval of convergence. Sum from k=0 to inf,…

A: Firstly, we find the radius of convergence as shown on board.Therefore, series is convergent for…

Q: (a)If Sn is a convergent sequence, then |Sn| is also a convergent sequence and (b) State the…

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Q: (i) Show that the sequence {2-1}=11 nis monotonic. (ii) Is it bounded above and/or below? Give a…

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Q: 5n 3) Determine if the sequence a, = converges or diverges. If it converges, find the limit 2n +1…

A: Explanation of the answer is as follows

Q: Determine whether n+1 converges or diverges. Give reasons for your answer.

A: Given: Here, an=n+1n2n. Notice that an=n+1n2n≈1n32. Now,                  limn→∞n+1n2n1n32=limn→∞…

Q: A. Consider a cone with radius of 17 cm and height 43 cm. Find the change in the volume of the cone…

A: A. given that radius of cone,  r=17cm height of cone, h=43 cm volume of cone is…

Q: 23п+1 converges. If it converges, find its exact value. 2. Determine whether or not the series S =…

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Q: 3 + 5n2 23. ая n+ n²

A: Basic series test

Q: 2n² converges or diverges. Use the Limit Comparison Test to determine whether the series n3 + 3 n=1…

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

Q: k$ – 4 13. Use the Limit Comparison Test to determine whether the series k° +7 converges or…

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Q: The alternating series (-1)" . converges. (You do not need to prove this, but you can if you 1 3" n…

A: Here, the given series is: ∑n=1∞(-1)n13nn Now, the given series is an alternating series with…

Q: (n!)² ". Show your work. (5) Find the interval of convergence of the power series (2n)!

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Q: 1. Evaluate the first few (4 or 5 should be enough) terms of the following sequences {an} use a…

A: Recall: A Sequence is convergent if the limit of the sequence <an>exists as n→∞. If the limit…

Q: 8. Suppose theory indicates that the sequence (Pn) converges to p of order 1.5. Explain how you…

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Q: Q1 a) By using the definition of the convergence s ?quence, show that whether the sequence 2n n-1…

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Q: Does the series converge absolutely, converge conditionally or diverge? k³ + 9 k=1 O diverges…

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Q: 14 3" n=1 Determine whether the series converges, and if it converges, determine its value.…

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Q: 5-4 To test this series for convergence, Σ n=1 You could use the Limit Comparison Test, comparing it…

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Q: Determine whether the sequence{5k(n+4) sin + 4} is convergent (find the value it converges), k(n+4)…

A: we know; limx→0sinxx=1

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: Does the seriesE (- 1)". 1 converge absolutely, converge conditionally, or diverge? n+9 n= 1 .....…

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Q: Identify two subsequences of ((−1)^n + 1/n) which converge to different limits. You should include…

A: Let the given sequence is Sn=-1n+1n We have to find two subsequences of given sequence that converge…

Q: SELECT ALL APF (2n +1)" A) converges by root test B) converges by Alternating Series Test C)…

A: To find the convergence of the series

Q: [1-(-1)" | (g) n+1 Converges or Diverges: limit (If Converges): (h) Èl-(-1)" n+1 n=1 Converges or…

A: As per our guidelines, i can answer only obe question. Since part g and h are the parts of a same…

Q: determine whether the sequence converges or diverges.if it converged find its limit.  {e^n/(n+4)}

A: Given:Given that  an=enn+4To find:we have to check the sequence is convergent or…

Q: 12 Determine whether the sequence an = 22 +...+ n3 n2 converges or diverges. If it converges, find…

A: an=12n3+22n3+......+n2n3 Now,…

Q: Find the values of x such that the 00 series > 2-n(x-1) converges, and n=0 for those values of x…

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Q: 15.) Suppose that a (x-2) converges when x=-3, then what is the smallest possible interval of k=0…

A: The answer is :

Q: Determine whether the sequence{5k(n + 4) sin( )+ 4} is convergent (find the value it converges),…

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Q: Determine whether the given sequence converges or diverges, and clearly state your answer. If the…

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Q: Does the series E (-1)"n converge absolutely, converge conditionally, or diverge? n= 1 Choose the…

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Q: 1. Evaluate the first few (4 or 5 should be enough) terms of the following sequences {an}–use a…

A: The given sequences are,a) an=2n2-3n+15n2+1b) an=-23n

Q: 00 (2х+3)" 2 2n+n-1 n=1

A: Given series is ∑n=1∞(2x+3)n2n2+n-1

Q: ( n2 1+ 2n² ]

A:

Q: Does the series converge absolutely, converge conditionally, or diverge? n=1 Choose the correct…

A: The given series is absolutely convergent since the corresponding series of absolute value is…

Q: sink Lk=1 k3

A: We have to check the convergence

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

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Q: 5 2n Determine if the sequence {4} converges or diverges. If it converges, find its limit: 3n 7…

A: To determine the limit of the sequence.

Q: Using the definition of convergence to show: If Sn is a convergent sequence, then |Sn| is also a…

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Q: 35 G1FTCARD Find the center a, the radius of convergence R, and the interval of convergence I for…

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Q: Using only the € – N definition of convergence prove that the sequence (a,)nɛN given by the formula…

A: We are given a sequence as : an = 5n7/7n And we have to show that the given sequence converges to 0…

Q: (a) Does the sequence converge? If so, find the limit and circle your final answer. If not, explain…

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Q: Use the Comparison Test to determine if the series Σ 5n Cos 2n n3 + n2 + 1 n=1

A: By looking at the series we get that the series is similar to ∑n=1∞1n2. So,                 limn→∞…

Q: Evn(5x + 4)" Find the radius of convergence R. R = (Enter "infinity" if the radius is infinite.)…

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Q: Vn2 + 1 Prove that the sequence {an}n=1 converges by following the following sequence of steps. n…

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Q: diverges if it is true. an n=1 Suppose > an converges. Assume the terms an are non-zero. Prove > n=1…

A: Consider the given information: Let ∑n=1∞an is convergent series. The terms of an are non-zero. To…

Q: 4n Find the limit of the sequence an = 4n and then determine if the Divergence Test applies to the…

A: By using statement of divergence test for series we solve the given problem.

Q: 2n + 5 Jse the definition of sequence convergence to prove this sequence converges: 6n 3

A: Concept:

Q: 1+9n² b) Determine whether the sequence a, = converges or diverges. If it converges, %3D 1+n find…

A: The given sequence is: an=1+9n21+n2

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.