One of the following sequences is converges : tan 'n 100 S1 A? O {(-1)" S 5n2 +1100 31 n-3 O {(-1)". n!};"

Q: converges to 0 Select one: True False

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Q: How many terms of the convergent series E=41/(n(In n)) should be used to estimate its value with…

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Q: n+1 (-3)*1 3n n=1

A: Ratio test : Suppose we have a series ∑n=1∞ an then define  c=limn→∞ an+1an . If 0≤c<1 then the…

Q: How many terms of the convergent series should be used to estimate its value with error at most…

A: Given series ∑n=1∞7n1.1.

Q: cos (n) 4) Is an alternating series? Does it converge ? Does it converge absolutely? Explain…

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Q: Find the interval of convergence of the power series. (Be sure to ine your answer using set…

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Q: 11.) -1 n=1

A: In the given question we have to determine the convergence of the series ∑n=1∞e1n2-1. we will use…

Q: How many terms of the convergent series 2 should be used to estimate its value with error at most…

A: Please see the explanation below

Q: The series C,(x + 3)" converges at x = 2 and diverges at æ = -12. Based on this information, what…

A: Given series is ∑Cnx+3n converges at x=2 and diverges to x=-12 Since, at x=2 series converges Hence,…

Q: Find the interval of convergence of the series IM

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Q: The first image has the directions; for the image that has ((nx^n)/(n+1)), find the interval of…

A: according to the guideline we are allowed to answer only one .for the rest please repost…

Q: For each n E N= {1,2,3, ..}, define an (A)-cOs (규1). = COS COS n+1 1. Determine whether the sequence…

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Q: Find the radius of convergence for: (-1)"x" √n +7 n=1

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Q: Find the sum of the convergent series (m til tan tan

A: Find the sum of the given convergent series.

Q: > sin n=1 2.

A: Explanation of the answer is as follows

Q: The sequence {5},-1s: 00 n=1 Converges to 5 O Converges to O Diverges. O Converges to 10 15

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Q: The series 1(-1)" converges to 0. True False

A: We have to find if the given series is converges.

Q: Σ 42n - (x + 3)" is convergent if The given power series : 9n n=0 |(x+ 3)| < ( Write your answer up…

A: using the fact that power series is convergent whenever |x-a|&lt;R;  R is radius of convergence

Q: Show if the sequence converges or diverges using  L'Hôpital's rule…

A: A sequence is said to be converge if its limit  exists, otherwise diverges.L'Hospital rule:- If…

Q: ind the interval of convergence of the power series n+1

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Q: Find the interval of convergence for each power series. If the interval of convergence is finite, be…

A: Given a series ∑k=0∞ 1k! xk We need to find the interval of convergence of the given power series.…

Q: Find the sum of the convergent series by using a well-known function. Identify the function and…

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Q: oll Show that sequence {n} n = 1, where .... 1/1₂ 0₂0₂...) converges 1/1,0,0 :) 9 9... 1/ng...) in…

A: We have to show that the sequence xnn≥1 defined by ; xn = 1, 12, ..., 1n, 0, 0,...  converges to  x…

Q: How many terms of the convergent series 6. should be used to estimate its value with error at mos n=…

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Q: Example :- Find the interval of convergence of the following series 1. 2.

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Q: Find the sum of the convergent series tan - ( m til tan M=1

A: This is a telescoping series.  Whose sum is  2/π

Q: The series 2(- 1)"+1 converges n = 1 Select one: True

A: The given series is ∑n=1∞-1n+1

Q: What is the function represented by the power series from k=0 to infinity of (-1)^k(x^k)/(3^k)?

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Q: Find the interval which the power series is convergent. n=1

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Q: 1

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Q: First four partial sums of the series, then find the limit as n approaches infinity if the sequence…

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Q: Find the interval of convergence of -(x + 10)" n! n=0

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Q: How many terms of the convergent series E1 (1/n'.1) should be used to estimate its value with error…

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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…

Q: show that this converges 2srt(2)/(9801) ∑∞ n=0((4n)!(1103+26390n))/(3964n (n!)) = 1/pie (show each…

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Q: Determine the rate of convergence of the sequence an = sin (12) as n 0o. 2 37n 2 n2 1 O A. O(1/n^3)…

A: Given the sequence is αn=sin23n+2n2-1. Find the rate of convergence of the sequence.

Q: The series from n=1 to infinity of n(n+4)/sqrt(n^3+5n^2.  Does it converge or diverge?

A: Take n2  common from the denominator and then go ahead

Q: The first term of the sequence is x1 = cos(1). The next terms are x2 = x1 or cos(2), whichever is…

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Q: The radius of convergence of -2 (x+6)" is: n=1 (-5) " (n)

A: Radius of convergence is calculated as below, The correct answer is option 2 i.e., 5

Q: 701 Discuss the convergence of the given sequence: a(n) = sin- 2

A: Given sequence: a(n)=&lt;an&gt;=sinnπ2

Q: The series Cn(x + 3)" converges at æ = 2 and diverges at æ = –12. Based on this information, what…

A: Here center of the series is -3 so radius should be measured from -3

Q: determine convergence by intergral test   sum from 2 to the infinity of 1/n（ln n）^5/4

A: We have given the series

Q: What is the interval of convergence of the series + +∞ (x+3)" 2n O a. (-5, -1) O b. [-5, -1] O c.…

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Q: 15) Eni e 2. Us-

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Q: Determine the rate of convergence of the sequence an sin( +3 as n+ 00. %3D OA O(1/n) O B. O(n) OC…

A: The given sequence is: αn=sin2n+3n2-5    =2n+3n2-5-13!2n+3n2-53+...    =2+3nn1-5n2-13!2n+3n2-53+...…

Q: The sequence =n sin - converges Select one: True False

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