Finding the Interval of Convergence In Exercises 15-38, find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)
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- Think About It Without performing any calculations determine whether the following series converges Explain. 1 1 1 10,000 10,001 + 10,002arrow_forwardpower series: using the Ratio Test or the Root Test to determine the radius of convergence, and indicate the open interval of convergence.arrow_forward(a) Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally. nx" n=0 11" (a) The radius of convergence is. (Simplify your answer.) Tutoring Textbook Ask my instructorarrow_forward
- 00 Consider the series > a, where a, = (-1)*+7 In( 1 + - n n=1 Is the series (eventually) alternating? ? Are the terms of the series (eventually) nonincreasing in magnitude? ? What is the limit of the terms of the series? lim an = n-00 Based on your answers above, can the alternating series test be applied to the series? ? Using the alternating series test or other tests, does the series converge or diverge? ?arrow_forwardDetermine whether the geometric series is convergent or divergent. If it is a convergent, find its sum. 3n+1 (a) Σ (-2)" 6- 22n-1 (b) n=1arrow_forwardCalculus 2 Question: Determine whether the following series is convergent or divergent using thecomparison test. The comparison test must be used for full credit. Show your work.arrow_forward
- (-1)" n² In(n) Determine whether the series converges absolutely, converges conditionally, or diverges. Fully justify n=2 your answer.arrow_forwardFind the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma- separated list of values.) n = 0 (-1)"ni(x - 9)" 50arrow_forwardCalculus 2 Question: Determine whether the following series is convergent or divergent using thelimit comparison test. Justify your answer, and show your work.arrow_forward
- Geometric series In Section 8.3, we established that the geo- metric series Ert converges provided |r| < 1. Notice that if -1arrow_forwardetermine whether the alternating series Σ (-1)+1 n=2 1 3(In n)² converges or diverges Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. OA. The series does not satisfy the conditions of the Alternating Series Test but diverges because it is a p-series with p= OB. The series does not satisfy the conditions of the Alternating Series Test but converges because it is a p-series with p= OC. The series does not satisfy the conditions of the Alternating Series Test but diverges by the Root Test because the limit used does not exist. OD. The series does not satisfy the conditions of the Alternating Series Test but converges because it is a geometric series with r= OE. The series converges by the Alternating Series Testarrow_forwardFind an infinite series (using the geometric form technique) that represents the fraction: 3 2-5x Give the interval of convergence for the power series you found in part(a)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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