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      <text>8.3.9 (Example of infinite series)</text>
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      <text><![CDATA[<h3>Example</h3>
<p>What is the value of \(\displaystyle1+\frac14+\frac1{16}+\frac1{64}+\cdots\)?</p>

<h3>Solution</h3>

<p>As we noted earlier, this is the geometric series with \(a=1\) and \(r=\frac14\). So using the formula,
\[ 
1+\frac14+\frac1{16}+\frac1{64}+\cdots = \frac{a}{1-r} = \frac{1}{1-\tfrac14} = \frac{4}{3}. \]
In particular, notice that this means the shaded area in the picture above is \(\frac13\) of the total area.</p>]]></text>
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