Suppose that the power series
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- Find the radii of convergence for each of the following power series. (a) (b) (c) n=1 n(x - 1)" 2n (n-1)x", n=1 Hint: The radius of convergence is 1. Explain why you can show this by checking that the series converges for x = -1, but diverges for x = 1. To show the latter, it is helpful to recall that (1+1)* S.M. ≤n. n=2 (x - π)" n(n − 1)*arrow_forwardpart D E needarrow_forward2. Consider the power series > ak(x + 2)*. Assume that we know that the series ak converges, but that k=0 k=0 ar(4*) diverges. k=0 (a) Does the power series converge at x = -1.3? Explain how you know, or explain why you don't have enough information to answer the question. (b) Does the series > ak (5)* converge or diverge? Explain how you know, or explain why you don't have k=0 enough information to answer the question.arrow_forward
- a, b and c please. I'm very confusedarrow_forwardFind the exact interval of convergence for the series in Example 6. Tell clearly using what method when it converges and and what method if diverges when checking for the interval.arrow_forward1. 3 33 34 65 why does this series converges?arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning