Does this series converge? Prove your answer 1 (2) Σ Vn3 + 3n2 n= 1 3/n3 + 3n2 (b) Σ n=1

Q: 5k 3 k=1 k4+1 k%3D1 co

A: Follow the steps.

Q: (c) Which of the following series converge? Justify any assertions that you make. (1) 3n (ii) n+1 3n…

A: I have given all the solution with the help of different tests.Final solution is in boxes.

Q: Use the Comparison Test to determine if the series Σ 5n – cos 2n 2 n3 + n² + 1 n=1 converges or…

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Q: 3. Determine which of the following series converge: (a) ( d) Σ 50 + 2n n= n=1 n O n (e) n=1 (2n2 –…

A: Please note that according to guidelines only first 3subparts is solved.

Q: Solve for the value of "b" in the equation: * (12) + b 11 Your answer

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Q: Find the series' radius of convergence. (х-3)п Σ n43n n= 1

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Q: Use the limit comparison test to prove that the series converges or diverges. (a) 2n +4n-n² 5n+n³…

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Q: Use the Comparison Test to determine if the series converges or diverges. 00 Σ 5n – cos2n - n3 + n²…

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Q: Which one of the following series is divergent? 1 1 (A) E (B) E 2n + n + 1 n2 + Vn n=1 n=2 1 (C) E…

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Q: Find the series' radius of convergence. (x -3)n (an)! n=1 0o, for all x 00 O 2 O 1

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Q: Use the integral test to determine if the series converges or diverges. Σ 1 5 n=1 (n + 2)7 8.

A: This is a problem of series and sum calculator. By using integral test we will identify the nature…

Q: 27 1. Let f(x) = (1 – 2)?* (a) Express f(z) as a power series. (b) Using the result in la, find the…

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Q: sin² n (2) Σ01 n=1 2n

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: n=1 sin(1/n) 3n+√√√n

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Q: 2. Use an appropriate test to determine if the series converges or diverges ∞ Σ n=l 3 1 + 2n

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Q: Determine if the given series converges conditionally or converges absolutely or diverges. (b) Č…

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Q: an = (-1)" η2 + 3 3η2 + 2n + 1

A: To determine if the sequence is convergent or divergent, we can examine its behavior as n approaches…

Q: +oo 1 ( a) Σ 4n2 – 8n + 3 n=1

A: Solution 1: Given that ∑n=1∞14n2-8n+3 Let un=14n2-8n+3 and vn=1n2

Q: 1. Show that the series converges uniformly on [0, 2]. 8 n=1 nx² n³ + x³

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Q: Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power series…

A: Rewrite the given expression using a single power series whose general term involves .

Q: Apply the ratio test to determine whether or not the series converges. (−1)n-13n 2 n² 8 n=1

A: Ratio test is used

Q: Use either the ratio test or the root test to determine whether the series converge or diverge. k 3k…

A: (a) Consider the series ∑k=1∞3k+12k−5k Root test:- Let ∑ak be a positive term series such that…