From d13605500dac2e1e6aa53dd7494af8e209acbd26 Mon Sep 17 00:00:00 2001 From: xianliticn Date: Thu, 16 Apr 2026 21:22:20 +0800 Subject: [PATCH] =?UTF-8?q?Update=20=E6=96=87=E7=AB=A0=20=E2=80=9C?= =?UTF-8?q?=E4=BD=BF=E7=94=A8=E5=BD=92=E7=BA=B3=E6=B3=95=E8=AF=81=E6=98=8E?= =?UTF-8?q?=E4=BA=8C=E9=A1=B9=E5=BC=8F=E5=AE=9A=E7=90=86=E2=80=9D?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- content/blog/使用归纳法证明二项式定理.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/content/blog/使用归纳法证明二项式定理.md b/content/blog/使用归纳法证明二项式定理.md index f6e2b1f..e825cc6 100644 --- a/content/blog/使用归纳法证明二项式定理.md +++ b/content/blog/使用归纳法证明二项式定理.md @@ -22,14 +22,14 @@ $$ 试图使左右两边相等,需要使得左边分母为$k!(n+1-k)!$,所以通分得: $$ -\begin{align} +\begin{align*} & \frac{n!}{(k-1)!(n-k+1)!} + \frac{n!}{k!(n-k)!} \\\\ &= \frac{n!k}{k!(n-k+1)!} + \frac{n!(n-k+1)}{k!(n-k+1)!} \\\\ &= \frac{n!k+n!(n-k+1)}{k!(n-k+1)!} \\\\ &= \frac{n!(n+1)}{k!(n-k+1)!} \\\\ &= \frac{(n+1)!}{k!(n+1-k)!} \\\\ &= \binom{n+1}{k}. \tag*{$\blacksquare$} -\end{align} +\end{align*} $$ 随后证明二项式定理