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.)26.
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- Determine whether the sum of the infinite series is defined. k=115(0.3)karrow_forward6"x" Consider the series n! n=0 (a) Find the series' radius and interval of convergence. (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally? (a) Find the interval of convergence. (Simplify your answers.) VIarrow_forward(-1)* /ī Given the series E " determine if the series converges conditionally, converges absolutely or diverges and select the test used to make your decision. Select the correct choice from each dropdown.arrow_forward
- 00 ()" Determine whether the alternating series 2 (- 1)" converges or diverges. n= 1 Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The series converges by the Alternating Series Test. B. The series does not satisfy the conditions of the Alternating Series Test but converges because it is a geometric series with r= C. The series does not satisfy the conditions of the Alternating Series Test but converges because it is a p-series with p = D. The series does not satisfy the conditions of the Alternating Series Test but diverges because it is a p-series with p = E. 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.arrow_forwardUsing the root test, the series E(-1)"(1-2) n2 (A) The root test fails. (B) Converges conditionally (C) Diverges (D) Converges absolutely (E) None of the above. A O B O .C D O E Oarrow_forward3-22 Find the radius of convergence and interval of conver- gence of the series.arrow_forward
- НОМЕWORK Determine the series converges or diverges, and if it converges find the sum k! A (2k)!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_forward2n=1 n2 +00 4-n (a) Determine whether the sequence is 2n+3)n=1 (i) (ii) (iii) (iv) increasing or decreasing; monotone; bounded and convergent. (b) Use the divergent test to show that the series +00 п+1 n=1 diverges. (c) Use the indicated convergence test to determine if the series is convergent or divergent. n+1 (i) Integral Test 50n (ii) Ratio Test n! (d) Find the interval of convergence and radius of convergence of the power series 00 k! k=0arrow_forward
- Real Analysis II: Prove whether the series converges or diverges Please follow outline in other photo!arrow_forwardDetermine the convergence or divergence of the series. (If you need to use ca or -ca, enter INFINITY or -INFINITY, respectively.) (-1)" lim O converges O diverges Need Help? Read It Watch itarrow_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_forward
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