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: Construct the inverse matrix (if it exists) for the following matrices: [12 61 (а) А %— 4 2. 1 -2]…

A: We will find out the required solution.

Q: b) Use the Ratio Test to determine if the series converges diverges. or n5" (2n + 3)ln (n + 1) n=1

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Q: Determine the interval of convergence for the power series below Σ ΣΠΟ n(x + 2)n 3η n=0

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Q: Use the Comparison Test to determine if the series Σ 5n – cos 2n 2 n3 + n² + 1 n=1 converges or…

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Q: 3. Determine which of the following series converge: (a) ( d) Σ 50 + 2n n= n=1 n O n (e) n=1 (2n2 –…

A: Please note that according to guidelines only first 3subparts is solved.

Q: (4) Σ=o (−1)n+7 n2+3 1/1

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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: Use the Integral Test to determine if the series 1 Σ (n +2)°/¾ n=1 converges or diverges.

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Q: Decide whether the following series converge or diverge; in the case of convergence, indicate…

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Q: 3. Determine whether the following series converges, and if so, find its sum. 1 ( a) Σ27l-n 4 (b) (n…

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Q: +00 4+ cos² n 1. 3n – Vn n=1

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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: Q. 5 - Using the converges tests, determine whether the following series converges or diverges n=1…

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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: Determine whether the series is convergent or divergent by using an appropriate test: cos(2n²+3)+2…

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Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, %3D {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3,…

A: A function is continuous if and only if inverse image of every open set is open

Q: 6. Determine if the following series converge. If so, determine the limit. (a) E(1-(-1)*+2) i=1 (»)…

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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: Find all values of z for which the following series converge. (a) L (1+z) n (n+2) (n+5)3n n=1 (6) L…

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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