Suppose that the power series ck(x x0)k has a fi-nite radius of convergenceR, and the
Chapter 9, Problem 57(choose chapter or problem)
Suppose that the power series \(\Sigma c_{k}\left(x-x_{0}\right)^{k}\) has a finite radius of convergence \(R\), and the power series \(\Sigma d_{k}\left(x-x_{0}\right)^{k}\) has a radius of convergence of \(+\infty\). What can you say about the radius of convergence of \(\Sigma\left(c_{k}+d_{k}\right)\left(x-x_{0}\right)^{k}\)? Explain your reasoning.
Equation Transcription:
Text Transcription:
Sigma c_k (x-x_0)^k
R
Sigma d_k(x-x_0)^k
+ infinity.
Sigma (c_k + d_k)(x-x_0)^k
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