a) Use the divergence test to determine whether converges or not. (-1)**'n n(3n² +1) b) Use alternating series test to determine whether c) Use the ratio test to determine whether F-1)"(n+1) n(n+2) converges or not.

Q: 5) f(x) = %3D 3-х

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Q: e Σ k=1 3.

A: The objective is to determine whether the series converges using any appropriate test ∑n=1∞ennn

Q: 3. divergent. En=1 Determine whether the series is convergent or

A: For the solution of the problem follow the next step.

Q: 1 Given that x" with convergence in (-1, 1), find the power series for with center 0. 1 - x 1- 2x7…

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Q: Determine whether the series converges using any appropriate test. Identify the test for convergence…

A: To determine the convergence of the series ∑n=1∞ennn Concept used: The root test

Q: Find a power series representation for the function. (- X - 1 f(x) %3D X + 7 f(x) = 1 + n = 0…

A: The given function is f(x)=x-1x+7 We represent this function as a power series, f(x)=(x-1)17+x…

Q: 4. Determine a power series representation of f(x) = (1+x*)- and o interval of convergence. %3D

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Q: 1 Does the series ) converge absolutely, converge conditionally or diverge? kº + 7 k=1 diverges…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1 is convergent or Use the Integral Test to determine whether the series ) (u u)u E=u divergent. You…

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A: The given function is, f(x)=71-x6 The function can be written as an infinite sum, if we write the…

Q: Determine whether the series converges using any appropriate test. Identify the test for convergence…

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Q: 00 Give an example of a divergent series> a, with lim a, 0 or explain why such a series does not…

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A: Use the quotient rule for derivative to determine the power series for f(x) centered at 0. Power…

Q: Use the Ratio Test to determine whether the series is convergent or divergent. 4nt 2) Identify lal.…

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Q: Determine whether the series converges or diverges if it converges find the limit. 1. n– 1 Σ n=1 3n…

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Q: 2. Σ- n3D0 (n+1)4 If the series converges, use the Integral Test can be used to show convergence

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Q: Use the power series 2(-1)"x^, \x| < 1 n = 0 1 + x to find a power series for the function, centered…

A: The given function is: f(x)=arctan(7x)So,f'(x)=71+(7x)2 Now, use the given series by replacing x by…

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A: Given that 11-x=∑n=0∞xn with convergence in-1,1 .

Q: Use an appropriate test to determine whether the series is convergent or divergent.  infinity…

A: Given a series : ∑n=1∞ n2+2n-12n2+3n We need to find if it is convergent or divergent.

Q: 1. Determine whether the resulting series when x = -4 absolutely converges, conditionally converges,…

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Q: Use the power series 00 1 2(-1)^xn, \x| < 1 n = 0 1 + x to find a power series for the function,…

A: Consider the function  gx=1x5+1 To find : Power series of g(x), centered at x=0

Q: Determine whether the series converges absolutely or conditionally, or diverges. 00 (-1)" Vn + 8 n =…

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Q: 1 Given that Σ x" with convergence in (-1, 1), find the power series for with center 1 - x 1- 7x8…

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Q: Determine the convergence or divergence of the series. 2 arctan(n) n = 1 Σ converges O diverges

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Q: Determine if the series converges or 1 sin [(2n+¹)] diverges: If the Σ n=1 n series converges,…

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Q: 00 k k 2. Σ (- 1)- k+1 k=0

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Q: 4n+1 Use a comparison test to determine whether the series is convergent or 3n – 2 - nt.

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Q: Q2/ Use the Integral Test to determine whether the series convergent or divergent. - 15

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Q: Determine whether the series converges using any appropriate test. Identify the test for convergence…

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Q: Use the power series Σ 1 1 + x 2(-1)^xn, \x| < 1 n = 0 to find a power series for the function,…

A: Given that, the function is gx=∑n=0∞1x9+1 centered at 0. Use the given power series to obtain the…

Q: Use the power series Σ 1 1 + x 2(-1)^xn, \x| < 1 n = 0 to find a power series for the function,…

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Q: 2. Determine whether the series converge or diverge, using the Ratio Test or Root Test. If the test…

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Q: 4. Using the integral test determine whether the series is convergent tan-(n) 1+ n? n=1

A: The given series is: ∑n=1∞tan-1(n)1+n2

Q: 1 Given that Σ x" with convergence in (-1, 1), find the power series for the function with the given…

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Q: Determine whether the series converges absolutely or conditionally, or diverges. 00 Σ (-1)" Vn + 1 n…

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Q: Use the root test to determine whether the series 2n 4n + 9 converges or diverges. 9n + 2 n=1 Since…

A: Root test : Suppose that we have series ∑ an .Define,                 L = limn→∞ ann = limn→∞ an1n.…

Q: rnatin

A: Introduction:   Let us suppose we have a series an as well as an=(-1)nbn or an=(-1)n+1bn, where bn≥0…

Q: 7. Find the first four terms of the Maclaurin series for f(x) = e2x. Show your work. Write your…

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Q: Use the power series 1 -Σ (-1)^x, x < 1 1 + x n = 0 to find a power series for the function,…

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Q: 1. Determine whether the series is convergent or divergent. Ifit is convergent, find its limit. *…

A: Convergent Limit=0

Q: Use the power series 00 1. =2(-1)x", \x\ < 1 1 + X to find a power series for the function, centered…

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Q: Use the power series 1 %3D 1 + X n = 0 to determine a power series, centered at 0, for the function.…

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Q: Use the power series 2(-1)"x", Ix| < 1 n = 0 1 + x to find a power series for the function, centered…

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Q: Determine whether the series is convergent or divergent by using the specified approach. n² +n+3 а)…

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Q: Use the power series 1 (-1)"x", \x| < 1 n = 0 1+x to find a power series for the function, centered…

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Q: 2. Determine the convergence or divergence of the series Σκ k = 1 Convergent A. Divergent В.…

A: The given series is ∑k=1∞k-52

Q: 1. Determine whether the series converges using any appropriate test. Identify the test for…

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Q: 1 b) Determine whether the series 1+-+-+-+-+… is convergent or 1 1 1 3 4 divergent.

A: Series is written as the sum of term of sequence where sequence is the list of numbers. Series are…