4. Use a comparison test to determine whether the series converges or diverges. (a) E 1+ In n In(e" – 1) n=1 sin n (b) n! + 3n+1 n=1 n3 (c) Vn7 +n+3 n=1

Q: 3. Let F(x) = sindt. cx (a) Show that F(x) = x- 3.3! x5 + by integrating an appropriate power…

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Q: 3. Let F(x) = sindt. (a) Show that F(x) = x −· 3.3! 5.5! 7.7! + by integrating an appropriate power…

A: The objective of this question is to express the function F(x) = sin(x) as a power series and then…

Q: 5. (a) Determine which of the following series converge and which diverge. n³ + 2n² + 3n+1 (n + 2)³…

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Q: For what values of x does the series converge conditionally? Σ n=1 (x-3)^ √n O A. x=2, x = 4 O B.…

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Q: 2. Use an appropriate test to determine if the series converges or diverges ∞ Σ n=l 3 1 + 2n

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Q: Determine if the given series converges conditionally or converges absolutely or diverges. (b) Č…

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Q: 3. Attach your work, in order from (a) to (1), on you series converge. Justify each conclusion with…

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Q: Apply the ratio test to determine whether or not the series converges. (−1)n-13n 2 n² 8 n=1

A: Ratio test is used