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      <text>9.0.7 (Pascal's triangle)</text>
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      <text><![CDATA[<h1>Pascal's triangle</h1>
<p>Moving on from factorials, one of the more useful structures when examining Binomials is <em>Pascal's triangle</em>. You may have already encountered this structure, but we will see later that this gives us an easy way to find binomial coefficients. It is named after the French mathematician Blaise Pascal, however it was already known to other mathematicians well before.</p>
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<p><strong>Pascal's triangle</strong> is the triangle where the entries of each row are the sum of the two entries above. This is shown in the following diagram.</p>
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<p><img style="display: block; margin-left: auto; margin-right: auto;" src="@@PLUGINFILE@@/Pascals%20triangle.jpg" alt="Pascal's triangle" width="442" height="325" /></p>
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<p>When using Pascal's triangle we enumerate the rows and columns so that we can identify each entry. The first row (the top row containing only the entry \(1\)) is the zeroth row. The entries in each row are numbered from the left also beginning with \(k=0\) and are staggered relative to the numbers in the adjacent rows. So for example, the 2 in the triangle is the entry in the 2nd row and 1st column and the first \(3\) in the triangle is in row \(3\) column \(1\). We denote the entry in the nth row and the kth column by \({n}\choose{k}\). We will see why we use this notation in the next section. For now let us concentrate on finding the different entries of the triangle. </p>]]></text>
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