Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement,enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you mustenter 1.)1. For all n > 2,2 <2. For all n > 1,3. For all n > e,4. For all n > e,arctan(n)n³In(n)nIn(n)n²and the seriesn²< and the series Ξ Σπ2n³and the series"n²n1n²3"and the series1nconverges, so by the Comparison Test, the series12 n³converges, so by the Comparison Test, the series >In(n)diverges, so by the Comparison Test, the series > diverges.nconverges, so by the Comparison Test, the series >Σn²_n²converges.arctan(n)n.³In(n)n²converges.converges.

we are not allow to solve more than 3 subpart in each question. Thank you

Answered: 1. For all n > 2,¹ <, and the series 2.…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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7. Consider the power series (-1)*+1g" n2 n=1 (a) The series converges when |x| R. Find R. (b) Does the series converge when x = R? What about when x = -R? Explain.
4. (a) How many terms of the given alternating series do we need to add in order to find the sum of the series correct to 5 decimal places? (That is, Jerror|< 0.000005.) Show your work! (b) Approximate the sum of the series correct to 5 decimal places. Show your work! 7 (-1)7+1. 2" (n!) n=1
6. Suppose that {an} is a sequence of nonzero real numbers. Suppose that > ak is a convergent series. Explain why 1 must be a k=1 ak k=1 divergent series.
+oo (x+ 7)" if the given power series is convergent in=2 3 2" n n 1 at x = 9, is it conditional or absolute? Give a reason how - and why.
12) There is one special “family” of series for which, if the series converges, we can determine the exact value of the series. This is the family where it really matters that we know the bounds of the summation. What family is this?
1. In this problem, you'll look at the series > 1 )J: One can visualize this series as area, by drawing a k5/4 * k=10 box of area 103/4, a box of area 134 and so on. 115/4 (a) There are two ways to draw the series (as boxes) in question. Draw each of them together with the graph y= 34 on two different graphs. x5/4 (b) Use the picture to write an inequality comparing >) 1 to an improper integral. Check the k5/4 k=10 bounds of your improper integral carefully, and be sure you are comparing on the same domain. (c) Is the improper integral you wrote in (b) convergent or divergent? Explain. (d) Using the inequality you wrote in (b) and your answer to (c), what (if anything) can you conclude 1 :? about the convergence of 2 k5/4 k=10 (e) Repeat (b)-(d) with your second picture.
10. For each series determine if it converges or diverges. In each case, show what test you are using and how you are using it. a. 00 > [2 In(n) – In(2n² + 1)] n=1 b. п!п! п! (Зп)! n=0
3) Ž (-e)" x"+1 What values of x make the series convergent, absolute convergence, conditional convergence, or divergence of the following series?
4. Does the series formed by subtracting the series 1 from the series 2n - 1 n=1 n3D1 converge? Give reasons for your answer.
Najabhai

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