Suppose that the series (a) (an+b)xn n=1 (b) Σan(x-7)n n=1 (c) bn(x-2)4n n=1 n=1 anx has radius of convergence 5 and bx has radius of convergence 9. Find the radius of convergence of the following series. R = R = R = n=1

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A: We have to determine the given series is convergent absolutely, converges conditionally or divergent

Q: 6. Are the following series convergent? Why? (a). (b) 00 n=1 α 2 (3n-1)1.3 n=1 n2 – 1 2η2 + η

A: The given series are ,  (a).        ∑n=1∞2(3n-1)1.3 (b).         ∑n=1∞ n2-12n2+n (.)  Necessary…

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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: 2. 201 3. Σ. 1 n(x-5)" 4" 2n n=1 nn

A: Note: As per our guidelines, we can solve first question. Please repost the remaining questions.

Q: Suppose that the series. anx has radius of convergence 5 and (a) n=1 (c) (b) an(x-7)n n=1 (an +…

A: The series ∑n=1∞anxn has radius of convergence  5 and series  ∑n=1∞bnxn has radius of convergence…

Q: Consider the following four series A =(2x)", B = E(2.r)", C= (-1)" (2x)", D = (-1)" (2.x)*" n n=1 n…

A: As you asked multiple sub part I only solved first three sub parts

Q: (a) Give an example of a series with nonnegative terms where > ak diverges but E a% converges. k=1…

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Q: Determine which of the following infinite series converge: Inn (a) (15 points) Σn-1 n (2n + 1) (2n −…

A: To determine whether the series ∑n=1∞​n(2n+1)(2n−1)lnn​ converges or diverges, we can analyze its…

Q: Consider the series a, where n=1 (6n + 2)7"+3 an = 10" In this problem you must attempt to use the…

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Q: For the power series Σn=1 (–3)” n find its interval of convergence. √n

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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: (a) Define the radius of convergence of a complex power series. (b) Compute the radius of…

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A: We need to find the Taylor series of f(x)=log3(x+1) with a=0. .

Q: What are the first non-zero terms of the Taylor series, the power series written in sigma notation,…

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