docs: update education/mathematics/binomial-theorem

education/mathematics/binomial-theorem.html

@@ -2,7 +2,7 @@
 title: 二項式定理 (Binomial Theorem)
 description: 
 published: true
-date: 2026-02-11T17:30:42.340Z
+date: 2026-02-11T17:32:23.010Z
 tags: 
 editor: ckeditor
 dateCreated: 2026-02-11T17:24:46.603Z
@@ -208,4 +208,28 @@ dateCreated: 2026-02-11T17:24:46.603Z
 <figure class="image"><img src="data:image/png;base64,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"></figure>
 <p><span style="font-family:Arial, Helvetica, sans-serif;">The coefficient of x<sup>12</sup> is 12,005.</span></p>
 <p>&nbsp;</p>
+<h2><span style="font-family:Arial, Helvetica, sans-serif;">Non positive power expansion</span></h2>
+<figure class="image"><img src="data:image/png;base64,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"></figure>
+<p><span style="font-family:Arial, Helvetica, sans-serif;">If&nbsp;n &lt; 0 and |x| &lt; 1, another formula can be used:</span></p>
+<figure class="image"><img src="data:image/png;base64,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 truncated
+<p><span style="font-family:Arial, Helvetica, sans-serif;">The negative or fractional n is a series that does not terminate, an infinite series.</span></p>
+<p><span style="font-family:Arial, Helvetica, sans-serif;">The series is convergent, as the limit of it sums only when&nbsp;|x| &lt; 1.</span></p>
+<p><span style="font-family:Arial, Helvetica, sans-serif;">The expansion is not valid for&nbsp;</span></p>
+<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAXCAMAAABwKZJpAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjpmOjqQOmZmOmaQOma2OpDbZgAAZgA6ZjoAZjpmZma2ZpC2ZpDbZrbbZrb/kDoAkDo6nGYAkGY6kJC2kNvbkNv/tmYAtmY6ttvbtv//25A625Bm27Zm27aQ29uQ29u22//b2////7Zm/9uQ/9u2/9vb//+2///b8s2P6QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABWklEQVQ4T+1Ua3OCMBBMsFS01Sp9CK2toQT7MFj4/3+uuUswL3Ckn3szgUlyt+xujhDyH5c7cNwuDpdnYyafv/dUiNlmJI5MP6ZLKGq3NKvTKEMAQdV7ZDSrO1lR7djt44FNoVit9Ec92w3jiwg223wqB0JwXPgDEmAAkYw0a4UZD7t9lpPiICYlDsBEjWSfRNL3ZkVtYB+poFel/LZWgQZzmc/jr1dC6gQ11g/fSE5PtVgPqdrI7fa5cwNzwWyRuKUnssazQF2bXxenk3a/apFQZLuD5NSEdbiMYhthDCLBRnMP3pncoAvU0fcidY4r77nbpIG6JrXa2GtpqwtY/GmoK/4+p+INm0iF34lmzqO5oy1Eki6ySamJq860wsgLf0CXE4+ewGZ4QtiW6ZVOuvC09ahzGATpRN8q9c2YS0rfKq4+8lMsXrKPUUBV700ncducLscw8qjI6S9Kqh8918TatwAAAABJRU5ErkJggg=="></figure>
+<figure class="image"><img src="data:image/png;base64,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"></figure>
+<p><span style="font-family:Arial, Helvetica, sans-serif;">&nbsp;can be used instead.</span></p>
+<p>&nbsp;</p>
+<h3><span style="font-family:Arial, Helvetica, sans-serif;">E6 Example</span></h3>
+<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Q</strong></span></p>
+<p><span style="font-family:Arial, Helvetica, sans-serif;">Expand the followings in ascending power of x up to and including the term x<sup>3</sup>.</span></p>
+<p><span style="font-family:Arial, Helvetica, sans-serif;">State the range of values of x for which the expansion is valid.</span></p>
+<figure class="image"><img src="data:image/png;base64,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"></figure>
+<p>&nbsp;</p>
+<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>A</strong></span></p>
+<figure class="image"><img 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truncated
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truncated
+<figure class="image"><img src="data:image/png;base64,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"></figure>
+<p><span style="font-family:Arial, Helvetica, sans-serif;">For&nbsp;</span></p>
+<figure class="image"><img src="data:image/png;base64,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"></figure>
+<p><span style="font-family:Arial, Helvetica, sans-serif;">&nbsp;</span></p>
 <p>&nbsp;</p>