diff --git a/education/mathematics/binomial-theorem.html b/education/mathematics/binomial-theorem.html
index 7f7d680..46cbb80 100644
--- a/education/mathematics/binomial-theorem.html
+++ b/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
The coefficient of x12 is 12,005.
+Non positive power expansion
+
+If n < 0 and |x| < 1, another formula can be used:
+
+The negative or fractional n is a series that does not terminate, an infinite series.
+The series is convergent, as the limit of it sums only when |x| < 1.
+The expansion is not valid for
+
+
+ can be used instead.
+
+E6 Example
+Q
+Expand the followings in ascending power of x up to and including the term x3.
+State the range of values of x for which the expansion is valid.
+
+
+A
+
+
+
+For
+
+