Test the series for convergence or divergence using the Alternating Series Test. sin 1 n + n = 0 8 + Vn Identify bn: Evaluate the following limit. lim b. Since lim b, a o and bn + 1 O b, for all n, ---Select--- ? ? in

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A: In the question we have to find weather series is convergent or not and the value.

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A: We have to find if the given series is convergent or divergent.

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A: Here we have to test the given series is convergent or divergent.

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Q: Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the…

A: Alternating seriese test

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A: First I have written the Taylor Series of the given function and then find its  Radius of…

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A: Given:

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A: Integral test:

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A: The given function is: f(x)=x5+4x3+x, a=4f(4)=45+4(43)+4=1284f'(x)=5x4+12x2+1,…

Q: 1 51. g(x) using f(x) (1 – 2r)² 1- 2x

A: We will solve the problem in following steps

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Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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Q: 23) ΣΡ 1+n n%3D1 24) Σ1 sin () 25) E, 5" (2n-1)! m%32 n-(2n+1)! n%=D1

A: p-series converges when p &gt; 1 and diverges when p &lt; 1.

Q: Find the Taylor series for f(x) centered at the given valueof a. (Assume that f has a power series…

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A: Solve the following

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A: Given: 11+x=∑n=0∞-1nxn, x&lt;1 To find: Power series expansion for f(x)=lnx8+1 and interval of…

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A: We have to find the interval of convergence.

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A: Given 11+x = ∑n=0∞(-1)nxn = 1 - x + x2 - x3 + ...

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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A: As per the company guidelines we can solve first question. I hope that the given solution will help…

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Q: a) Find a geometric power series representation for the function 3 f(x)= and find its radius of…

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

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A: The power series representation of the following function is to be determined.

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