Chapter 1: Problem 19
\(\sum_{0}^{\infty} 8^{-n}\left(x^{2}-1\right)^{n}\) Method: Let \(y=x^{2}-1\). The power series \(\sum_{0}^{\infty} 8^{-n} y^{n}\) converges for \(|y|<8\), so the original series converges for \(\left|x^{2}-1\right|<8\), which means \(|x|<3\)
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Key Concepts
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