Decide whether the following series converge or diverge; in the case of convergence, indicate whether it is absolute: (a) n(1+i)" *-1 (21)" (b) ²2" =1(1+i)" (c) [7. n=1 VN

Q: Decide whether the following series converges or diverges. (a) L n00 5n-2021n² , 7" 4"

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Q: The series elnz) - e) converge to n=1 (a)Ve - 1 (b) e - et (c)Ve - e3

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Q: (b) Find the sum of each of the following series. 00 (i) > nx", , |x| < 1 n = 1 (ii) Σ 3n 8.

A: i).  To determine the sum of infinite series given by; ∑n=1∞nxn,|x|&lt;1 Consider the series…

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Q: Check the convergence of the following power series, find the radius and interval of conver- gence:…

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Q: 6 (c) 5n n%3D1 3n2 + 12n - 6 5n4-3n2 + 8 (d)

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Q: (ax-b) n n=0 c2n If a = 2, b = 8, and c = 18.31 then the series is convergent if x < Round off the…

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Q: (b) Test the convergence of the series by ratio test. 00

A: Ratio rest is as follows

Q: Part IV: Determine whether the following series are convergent or divergent. Use the nth term test…

A: The main objective is to check the convergence or divergence of the series.

Q: [8]. Consider the series (-1)" – n+4 n(n + 3) * Is this series conditionally convergent, absolutely…

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Q: 1. Investigate the convergence and divergence of the following series, and obtain the sum upon…

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Q: Determine whether each of the following series converges. If it does, find its sum otherwise answer…

A: Step 1: Step 2: Step 3: Step 4:

Q: 2. Use root test to determine whether the following series is convergent or divergent: 00 Σ n=2…

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Q: For what values of x does the power series > converge? 5" n n=1

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Q: Σ (-1)"+1 n³+1 n=0

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Q: timate Σ (-1)" / (2″ + 7) to within an accuracy of 0.01. (Make sure to verify the series meets the…

A: Estimate sum (- 1) ^ n / (2 ^ n + 7) to within an accuracy of 0.01. (Make sure to verify the series…

Q: 1. Find the first partial derivatives of the following functions: a. f(x, y, z) = 3x²/² b. f(x, y) =…

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Q: olutely convergent, conditionally convergent, or ergent. |(-3)n² / (n + 1)! E (-3)" / (2n² + 4") 2…

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