Which one of the following series is absolutely convergent? 2(-1)" n2+5 n n=1 00 3 2(-1)"- n=1 n+4 (-1) n-1 n3 n°+3 n=1 (-1)"-1, n=1 n + 3 O None of them

Q: Determine whether the following series are convergent or divergent. Explain explicitely. 00 1+n! (a)…

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Q: Which series given below converge conditionally. (-1)" n=2 n²+1 (-1)" 2 Inn 1) E-2 00 II) E, (-1)"…

A: For details solution see the  answer below

Q: The set of convergence of the power series Σ (x +5) n2(1+3") is O (A)[-8, -2] O (B) (-16/3,-14/3) O…

A: To find the convergence, we will use ratio test. D' Alembert's Ratio test: Consider the series ∑nan…

Q: Determine whether the series is convergent or divergent. If the series is c 5k +2k gk find its…

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Q: (Q6) Determine which of the following series are convergent. You may use the convergence and…

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Q: What are all values of r for which the series (-1)+1(r+2)" converges? n=1 (A) –1 <r < 1 (E) -3 < r <…

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Q: 7. Determine (with proof) if the following series is converging absolutely, converging conditionally…

A: The given series is ∑-1nn+1lnn+1.   The alternating series test states that if an is a positive…

Q: (-1)"4"+1,n+1 3n+1(n + 1) In this problem, we investigate the power series n=0 Σ (-1)"4"+lpn+1…

A: We have to find the power series.

Q: 19 * If the series > (-1)"a, is convergent and the seies an is convergent then n=1 n=1 we said the…

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Q: Consider the series Find an expression for an 72 720 an= (x-8)³ + (x-8)6 5-2! (x-8)⁹ (x-8)¹2 25-3!…

A: Given: ∑n=n0∞an=x-83+x-865·2!+x-8925·3!+x-812125·4!+ . . . We have to find an expression for an.…

Q: 15 - Use alternating series test (Leibnitz test) to decide that which ones of the following…

A: Leibnitz test. First and second series are convergent.

Q: (-1)"n(z- 4)" 3. Find the radius of convergence and interval of convergence for the power series 2n

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Q: 4 3. Let S = E(-1)n+11 and let S4 = E(-1)n+11. Then S4 < S since the next term in the series is…

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Q: Identify all of the convergent series below. (-1)" (1) 4n – 2 =1 - * (-1)"n (2) 4n – 2 n=1 (-1)" 00…

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Q: If the series >(-1)"a, is convergent and the seies is convergent then n=1 we said the series >…

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Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent.…

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Q: Consider the following series 00 1 (1) (2) ) (3) (-1)"n In n n(ln n)³ (n + 7) In(n + 7) n=2 n=2 n=2…

A: Given:

Q: (-2)1+3n(n+1) Test the convergence of Ln=2' by ratio test. n251+n

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Q: Which of the following is true? O A p-series is divergent if p > 1. none The series E(-1)" -1, 2 is…

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Q: Find the interval of convergence for the power series =1 (x-1)" 7"n

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Q: Which of the following series is conditionally convergent? (A) B n=1 Σ(-1)²+1 17+n √n n=1 sin(n) 7²…

A: Given that, (A) The series  ∑n=1∞sin(n)n2 ,  Since,   ∑n=1∞ sin(n)n2 ≤   ∑n=1∞ 1n2 which is a…

Q: 5. The series ∞ n=1 (n + 1)² n! ... (a) is Absolutely Convergent (b) is Conditionally Convergent,…

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Q: Find the interval of convergence for the given power series. (2 - 6)" n(- 6)" n=1 The series is…

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Q: Mark all of the series that converge. 0 0 U 0 n=1 ∞ (-1)" Σ n=1 n + n² (-2) ¹² n-2 Σ(-1)"n n=1 n=1…

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