Using a Power Series In Exercises 19-28, use the power series
to find a power series for the function, centered at 0, and determine the Interval of convergence.
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- Let an Does {a} converge? Does a, converge? 3n +1 Give an example of a divergent series E, where lim a =0. Does there exist a convergent series a, which satisfies lim a, # 0? Explain. When does a series converge absolutely? When does it converge conditionally? State the ratio test. State the root test.arrow_forwardCheck that series is convergent or divergentarrow_forwardFind the first term of : Ln=1(-1)n+1 (z+1)" 2%3D1 n -[(z+1)^2]/2 Z+1 no solutionarrow_forward
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- Tutorial Exercise Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R(x) → 0.] Find the associated radius of convergence R. f(x) = 9/x, a-3 Step 1 The Taylor series formula is f(a) + f'(a)(x − a) + f(a)(x − a)² + f(a)(x − a)³ +. ƒ(4)(a) (x-a)4 2! 3! 4! |-1 ✔ 2✔ -6 The function f(x) = can also be written as f(x) = (9), which has derivatives ƒ'(x) = (9)- f"(x)= (9) f"(x)= (9)- 3 24 24 f(4)(x) = (9) Step 2 X With a = -3, f(-3)= (9). f'(-3) (9)- X 32 f"(-3) = (9) X 33 f"(-3) = (9)- 34, and f(4) (-3) = (9) Submit Skip (you cannot come back) 35 andarrow_forward00 Give an example of divergent seriesan and b, such that (a, + b,) = 1. n=1 n=1 n=1arrow_forwardStudy the power series: - Using Limit Comparison Test show that this series converges when x = −2. - Justify if the series is absolutely convergent, conditionally convergent, or divergent at x = 12? - Determine the radius and interval of convergence of the power series.arrow_forward
- The function f(x) = 8x In(1 + x) is represented as a power series f(x) Σ Cna". n=0 Find the specified coefficients in the power series. C2 C3 C4 = C5 = C6 = Find the radius of convergence R of the series. R Question Help: Video Submit Question || ||arrow_forwardDetermine all values of a such that the series 1 Σ (n+1)[logi/2(n+1)] converges.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage