Use a test for convergence to determine whether the following series converge or diverge. n² – 2 (i) 2* k2 (iii) -1)"-1 Vn -1 (ii) ( ίv) Σ (iv) 3n² – 2 n3 +1 k! k=1 2n2 + 3 n=0 n=2 As part of your solution, clearly state which test for convergence is used.

Q: Σ (k+ 1) (k + 2) k=1

A: Ratio Test

Q: Test the series for convergence or divergence. n2 E(-1)". Σ n2 + n + 1 n = 1

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Q: Please solve all

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Q: Use the Comparison or the Limit Comparison test to show convergence or divergence of each series.…

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Q: 2 2 4 4 6 6 -=-X-X-X-X-X-X (1) K... 2 1 3 3 5 5 7 1 1 1 = 1- (2) + 4 3 5 7 9 n² 1 1 1' 2?' 3? 6 ?22…

A: Calculate the percentage error when using the first 10 terms of eachapproach. Which of the 3 series…

Q: 2. Determine the radius and interval of convergence of the power series +∞ (-2)(x+5)n-1 n² n=1

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Q: (d) 22n+1 п! n=1 (e) (-1)" arctan (n) Σ n2 n=1

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Q: (-1)* Consider the series (2k)! k=0 (-1)* to within 10-5 of the actual sum of the series. (You may…

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Q: 5. Determine whether each of the series converges conditionally, converges absolutely, or diverges.…

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Q: 2 (a) Use the Comparison Test to show that the series=1 4n3n²+3 converges. (You may use the fact…

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Q: (a) (b) m=0 11=0 (-1)" vn+1 (-1)" √√n+1 元+1 n²-3n+1

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