00 (b) Carefully determine the convergence of the series 2 (-1)" The series is 5n n=1 A. absolutely convergent B. conditionally convergent C. divergent OO0

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A: We have, the given series as ∑n=0∞75n On expanding the term, we get the result as…

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Q: Determine convergence or divergence of the alternating series. (-2)h 5n6+ 2n n-1 Diverges Converges

A: Given, ∑n=1∞-2n5n6+2n In an alternating series to show it convergence in these two condition…

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Q: Find the interval and radius of convergence of the power series (z - 5)k k2 k 1

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Q: 5. Find the interval of convergence for the series f(x) = E· (-1)*(x-3)" (n+1)2

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Q: Find the interval of convergence of the power series: ∞ n [²(+1²] (x + 1)n 1)"] 2n n=0

A: To find the interval of convergence.

Q: Find the interval of convergence for the power series (x – 3)" n6 + 8 n=0

A: We know by Ratio Test, the series ∑an is convergent if limn→∞an+1an < 1.

Q: Find the interval of convergence of the series. (x-1) 5n+ 4 n=0

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Q: Find the interval and radius of convergence of the power series E(-1)** (x+2)" п 2" n=1

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Q: Determine whether the alternating series converges. k + 1 2(- 1)k+1. 2k + 1 k=1

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Q: 4) Find the interval of convergence for the power series F(-1)"-'n 2" t. n=1

A: Given series is ∑n = 1∞(-1)n-1n2nxn

Q: 9. Find the interval of convergence and the radius of convergence of the power series (x- 8)" Σ n=1…

A: Given,    ∑n=1∞x-8nn.7n

Q: 2. Find the radius and interval of convergence of the power series: 7-"(10x - 1)" n=0

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Q: Find the radius of convergence and interval of convergence of the series ;(-3)x* -o vn+1

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Q: Find the interval of convergence of the power series (-1)"(n – 2) x – 2)" n² 2n n=3

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Q: Find the interval of convergence of the power series n3 n=1

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Q: . Determine the radius and interval of convergence of the power series E(-1)*+1 n3n

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Q: Find the interval of convergence of the series. (x - 8)" Σ 5+ 7n n=0

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Q: У7-"(10т — 1)" —п n=0

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Q: Find the radius of convergence and interval of convergence of the series. 2n=1 2"(n²+1)

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Q: 3. Find the radius of convergence and the interval of convergence of the series 00 (-3)"x" Vn + 1…

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Q: (-1)* Estimate the value of the convergent series with an absolute error less than 10-5. k! + 2 k=1

A: Solution is given below:

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A: Given,        ∑n=0∞x-5n4+9n

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Q: Give an example of two convergent series E1 *k and E1 Yk such that = *kYk diverges. Can this happen…

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Q: Determine whether the alternating series converges. Σ k + 1 7k + 1 k=1

A: ∑k=1∞(-1)k+1k+17k+1  Above Series is an alternating seriesApply Liebnitz Testlet   ak=k+17k+1…

Q: 5. Determine whether the series E -(-1)*52a÷1 converges absolutely, converges conditionally or 25n-2…

A: Explanation of the answer is as follows

Q: Find the interval of convergence of the series. (x-5) 5n+1 n=0

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Q: 4 5. Find a power series representation of the function and its interval of convergence. f(x) 2x+3

A: we have to find  the power series representation of this function and its interval of  convergence

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Q: 3. Find the radius of convergence and the interval of convergence of the series 00 (-3)"x" Vn +1 n=1

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Q: find the interval of convergence of the power series

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Q: (-1)"x2 Is The interval of convergence of the power series 22n! Select one: O a. (-00, 00)

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Q: 1. Find the interval of convergence of the power series E- xn n2

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

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Q: Find the radius of convergence and interval of convergence of the series –3)”.gn 'n + 1 n=0

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Q: 1. Determine whether the series ż 1 2n+1 1 2n-1) converges or diverges by examining the

A: Given series is ∑n=1∞12n+1-12n-1