Convergence of functional series 1. Prove that each of the following series converges absolutely: (a) 2" n=1 Σ (-1)"-1 п.3" (х — 5)" (b) n=1

Q: (d) Determine if the series 6 Σ(+)" 4 n=2 =onverges. If it is, find its sum.

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Q: ) For what values of x do the following power series converge? G(r) = (* - 2)" n5" n=1

A: By the ratio test Let an =(x-2)n/(n5n)      |an+1|/|an| =|(x-2)n+1/((n+1)5n+1)|/|(x-2)n/(n5n)|…

Q: Q2. (a) Find the following series interval of convergence and, within this interval, the sum of the…

A: Answer is mentioned below

Q: Determine which (if any) of the following series are conditionally convergent Α. Σ-1" sin (n) C.…

A: I just answered which are convergent

Q: Use interval notation to present the answers to these three questions. a) Find the set of real…

A: Note: As per our Guidelines, we can solve first parts as your all parts are not small.

Q: Which of the following series converge? 1 (1) E e n= 100 n 100 (II) (1) Σ 0.99999 n=1 n - 1.00001…

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Q: If the interval of convergence of the powe

A: Given, the power series                          ∑n=2∞(-1)n(x-c)n4nlnn

Q: (a) For which numbers x does the geometric series E(3x – 2)" converge? (b) To what does the above…

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Q: and identify the values of the interval for which the convergence is absolute or conditional. n? 00…

A: We will first find the radius of convergence and then interval of convergence

Q: (a) Briefly explain why each of the series below either converges or diverges. (-1)"-1 1/2 n=1 n²…

A: According to guideline we need to solve one question. The rest of the question should be reposted.

Q: (1) Find the radius of convergence and the interval of convergence of the following series Σ m=2…

A: The given series is .To find the radius of convergence and interval of convergence of the power…

Q: (1). The following series does it converge? (a). Enzo(5)". n=0

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Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent.…

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Q: 19. Find the radius of convergence and the interval of convergence of the power series ∞0 n=1 (x-4)"…

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Q: A. Convergent geometric series B. Convergent p series C. Comparison (or Limit Comparison) with a…

A: Note: As per the guidelines will be solving only 1st three subparts. Please repost for remaining.…

Q: Find the interval of convergence for the following series. Σ(3) 2η

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Q: Letf(x) be a polynomial with integral coefficients. Iff(1) and f(2) both are odd integers, prove…

A: Let us assume that  f(x)=0 for some integer x=k, then x-k divides f(x). therefore  f(x)=(x-k)g(x) ;…

Q: tan (n) – tan (n + 1) n=1 b) 2" + 3" 4" n=]

A: We have to find the sum of the given series