For what values of x does the series 1 1-,(x- 3) +(x – 3)² + …. + (x – 3)" + ...... ... converge? What is its sum? What series do you get if you differentiate the given series term by term? For what values of x does the new series converge? What is its sum?

Q: 3. Find the radius of convergence and interval of convergence of the series (3x + 2)" (a) n! n=1

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Q: Σ (n:)? The radius of convergence of the series (x- 2)2 is equal to ........ n=1 3" (2n) !

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Q: 2(– 1)*+1 k(k + 10) By the alternating series test, the series converges. Find its sum. k=1

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Q: +00 For what values of x do the power series (-1)"-1^_ converges. n=1

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Q: 10. Find the interval of convergence and the radius of convergence of the power series (x-4)" n·9"…

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Q: Find the radius of convergence and interval of convergencE of the power series. (2х — 1)" 26. E 5"…

A: Use ratio test for checking the radius of convergence  and interval of convergence .

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Q: The interval of convergence of the power series (-1)" (x-4)" Zn=1 is 00 4n+1 A. (3,5) В. [3,5) С.…

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Q: -- 4. For the geometric series [a+ar+ar2+ar3+ the series converge to: -ar"-1]. If a=1 and r 1/2 А.…

A: According to bartleby guidelines I can solve only one problem, for more solutions please mention it…

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Q: 2n+1 By using comparison test, test the series E to be: n(n+1)²

A: We have to solve given problem:

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Q: 10. Determine the interval and radius of convergence for the power series. Σ 2k (x + 2)k k2 k=1

A: Solution is given by using the ratio test as follows

Q: Within the interval of convergence, evaluate the infinite series. A. (e" – 4)" = on the interval n=0…

A: A) Consider the infinite geometric series ∑n=0∞xn. The series converges if -1<x<1 and the sum…

Q: Consider the series xn+1 3n n = 0 a. Find the interval of convergence for the given series. b. For…

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Q: 3* (z-2)* The radius of convergence of the series o is k-0 k!

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Q: 6. Find the radius and interval of convergence for the given power series. (2x – 6)* k2 00 k=1 I= R…

A: We will approach this problem using ratio test. Let ak+1 and ak represent the (k + 1)th and kth term…

Q: (-1)* Catalan's constant is defined by K = (2k + 1)2 * k=0 How many terms of the series are needed…

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Q: 2 For the telescoping series find a formula for the nth term of the sequence of (2k – 1)(2k + 1)’…

A: The sum of this series is 1.

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Q: For what values of x does the series below converge? What is its sum? What series do you get if you…

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Q: 1 Determine the convergence or divergence of the series - 3 n=1 yn° + 1 The series O A. Converges O…

A: Comparison test: Let ∑an be any series and  limn→∞anbn=L Where L is finite and positive, then ∑an…

Q: For what values of x does the series below converge? What is its sum? What series do you get if you…

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Q: Find the sum of the geometric series for those x for which the series converges. > (x - 2)n n=0 1 1…

A: Given Geometric series as ∑n=0∞x-2n

Q: n!x" 4. Find the interval of convergence of the power series n=1 IM:

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Q: Find the interval of convergence for the given infinite geometric series. 6+ 6 (x + 3) + 6 (x + 3)²…

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A: Given series is: ∑k=1∞-1k+1k To find the value of the series.

Q: 11) Find the radius and interval of convergence of (x + 3)" Σ the series n = 1 n!

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Q: Find the radius of convergence and interval of convergence of the series. (x – 4)" 72 E(-1)" Зп + 1…

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Q: Consider the series 2n Σ n=0 3n +1 by the test of divergence, O lim a, #0 , so the series diverges n…

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Q: 4. Consider the series (-1)"-1 n10" n=1 (a) Show that the three conditions given in the alternating…

A: Given: ∑n=1∞(-1)n-1n10n

Q: | of convergence of the series -1 (1+)"x"? What is the interval of -2e < x <2e а. оb. -1 <x <1 Ос.…

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Q: e the Direct Comparison Test to determine the convergence or divergence of the series. 5n 4n - 1 n =…

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Q: The radius of convergence for the power series (x – 3)²" is equal to 1. What is the interval of…

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Q: 1. Find the radius of convergence and interval of convergence of the series n(x+2)" 5n-1 n=1

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Q: 6. Find the radius of convergence and the interval of convergence of the power series E(-1)"n²(x –…

A: Given :

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Q: 00 If the series a x" +1 -has the radius of 5, then the radius of convergence of the "n+1 n=1 series…

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Q: n(n+1) 3n n=1

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Q: 1. For what values of b does the series 1+ 2b + b² + 2b³ + b4 + 2b5 + b6 ... converges? Find the sum…

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Q: 1. Find the interval and radius of convergence for the series. 1)k k- 5k k=0

A: Answer and explanation is given below..

Q: For what values of x does the series below converge? What is its sum? What series do you get if you…

A: We have to find the sum and derivative of the series.

Q: 20. Find the series radius and interval of convergence E1(x + 5)". For what values of x does the…

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Q: Find the radius of convergence and interval of convergencE of the power series. (x 25. E 2)" n=1 n"

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Q: 4 The terms of the Maclaurin series of the function f(x) = - -x are given by

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Q: 2. The series (2n)! = 6 n 0 2en+ (n!)°(2n+1) 7 = 6 (; + 1-3 1-3-5 2-4-6-7 2-3 2-4-5 has been…

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