Using a Power Series In Exercises 37-40, use the power series
to find a power aeries for the function, centered at 0, and determine the interval of convergence.
Trending nowThis is a popular solution!
Chapter 9 Solutions
Bundle: Calculus: Early Transcendental Functions, 7th + Webassign, Multi-term Printed Access Card
- USING ALTERNATING SERIES TEST PROVE THAT THIS CONVERGES.arrow_forwardUse the power series for the function, centered at 0, and deermine the interval of convergence: f(x) = - 1/(x+1)^2 = d/dx[1/(x+1)]arrow_forwardEXAMPLE 5 Binomial series Consider the function f(x) = V1 + x. a. Find the first four terms of the binomial series for f centered at 0. b. Approximate V1.15 to three decimal places. Assume the series for f converges to f on its interval of convergence, which is [-1, 1].arrow_forward
- (-3)" converges or diverges. Vn Determine whether n=1arrow_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_forwardLet a be a real number. Consider the series Σ Qn cos(n7); An, where an = 2n + 1 n=0 (a) Is it possible to find an a > 0 such that the above series is both absolutely convergent and conditionally convergent? Briefly explain your reasoning. Answers with reasoning (b) Find all a > 0 such that the series diverges. (c) Find all a > 0 such that the series converges absolutely.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage