?Suppose that the power series \(\sum c_{n}(x-a)^{n}\) satisfies \(c_{n} \neq 0\) for
Chapter 11, Problem 44(choose chapter or problem)
Suppose that the power series \(\sum c_{n}(x-a)^{n}\) satisfies \(c_{n} \neq 0\) for all n. Show that if \(\lim _{n \rightarrow \infty}\left|c_{n} / c_{n+1}\right|\) exists, then it is equal to the radius of convergence of the power series.
Equation Transcription:
∑
Text Transcription:
Sum c_n(x-a)^n
c_n neq 0
Lim_n rightarrow infinity |c_n/c_n+1|
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