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        "intro": "<p>In this Section we consider power series. These are examples of infinite series where each term contains a variable, \\(x\\), raised to a positive integer power, that is \\(\\displaystyle{\\sum_{n=0}^\\infty a_nx^n}\\) where \\((a_n)_{n\\geq 0}\\) is an infinite series of real numbers.&nbsp;<\/p><p><span style=\"font-size: 0.9375rem;\">We use the ratio test to obtain the <\/span><b style=\"font-size: 0.9375rem;\">radius of convergence<\/b><span style=\"font-size: 0.9375rem;\">, \\(R\\), of the power series, this is the result that the series is absolutely convergent if \\(|x|&lt;R\\), divergent if \\(|x|&gt;R\\), and may or may not be convergent if \\(x=\\pm R\\).&nbsp;<\/span><\/p><p><span style=\"font-size: 0.9375rem;\">Finally, we extend the work to apply to general power series when the variable \\(x\\) is replaced by \\((x \u2212 x_0)\\), that is, series of the form&nbsp;\\(\\displaystyle{\\sum_{n=0}^\\infty a_n(x-x_0)^n}\\). Note that here we say the series is 'centered' at \\(x_0\\)<\/span><br><\/p>",
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