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.)31.
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- Determine whether the sum of the infinite series is defined. k=115(0.3)karrow_forwardReal Analysis I must determine if the two series below are divergent, conditionally convergent or absolutely convergent. Further I must prove this. In other words, if I use one of the tests, like the comparison test, I must fully explain why this applies. a) 1-(1/1!)+(1/2!)-(1/3!) + . . . b) (1/2) -(2/3) +(3/4) -(4/5) + . . . Thank you.arrow_forwardfind the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)arrow_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_forwardDetermine if the series converges or divergesarrow_forward00 ()" 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_forward
- etermine 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_forwardadvance matharrow_forward
- How to do this?arrow_forwardNumber 31arrow_forward∞ Expand the function in a power series Σ anx" with center c = 0. Find anx". 7+6x n=0 (Express numbers in exact form. Use symbolic notation and fractions where needed. For alternating series, include a factor of the form (-1)" in your answer.) anxh Determine the interval of convergence. (Give your answers as intervals in the form (*, *). Use symbol ∞ for infinity, U for combining intervals, and appropriate type of "1 parenthesis (",") ", "[" or "]" depending on whether the interval is open or closed. Enter DNE if interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) x E =arrow_forward
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