(b) Discuss the uniform convergence and point-wise convergence of following series/sequence (Each step must be justified) Σ 1 n3 + nªx² n=1 • (-V2, v2] fn(x) = 1 – |1 – x²|² defined on

Q: (A calculator is not allowed for this problem) The function f is defined by the power series…

A: Given function .Note: According to the guidelines we are allowed to solve three sub parts at a time.…

Q: 3) Use the fact the Ex = if -1<x<1 to find series representations for each of 1-x the following…

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Q: . Find the power series representation of f(x) = 3 using the geometric series 3+x 1 f(x) = 1 - ",…

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Q: 6. Find the power series and determine the interval of convergence of 3x f(x): x2+x-2

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Q: 3) Use the fact the Er =;- if -1<x<1 to find series representations for each of 1-x the following…

A: Solve the following

Q: Let an (2n³ + 1) sinn n² +1 (1) Does the sequence (2) Does the series n=1 n² + 1 (2n³ + 1) sinn n¹ +…

A: Here we have given a sequence  where,

Q: Consider the series (-1)" (6x+5)" n=0 (a) Find the series' radius and interval of convergence. (b)…

A: We have to find- series radius and interval of convergence, values of x for which series converge…

Q: the following series for conve 2π) 6 3n 2x5x8 2x5x8x11

A: We have to consider the given series are convergent or divergent according to the given information

Q: (1) For each of the following power series, find the convergence radius: (2) Σ (b) (c) 178 √n (3η)!…

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Q: Part II: Determine if the following series are convergent or divergent. You should use each of the…

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Q: 8 (a) [-R, R) (b) (R-a, R+ a) (c) (a - R/2, a + R/2) (d) (a - R, a +R] (e) None of the above. n=0…

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Q: Find the interval of convergence for the series x + 5 27x3 81x4 + 7 +.. 9 O (1/3) <x s (1/3) О 113)…

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