Using a Power Series In Exercises 37-40, use the power series
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Calculus
- 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_forwardadvance matharrow_forwardAnalysis advance matharrow_forward
- Write a power series representing the function f(x) = : %3D 6-r f(a)= Σ Determine the interval of convergence of this series: (Give all intervals in interval notation.) Find a power series that represents f'(x) and determine its interval of convergence. f'(z) = E n=1 Interval of convergence: Find a power series that represents f f(2)dr and determine its interval of convergence. Sf(z)dr = C + Interval of convergence:arrow_forwardCalculus IIarrow_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
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