qingshuige-authors/qingshuige-hugo
2
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Update 文章 “使用归纳法证明二项式定理”
All checks were successful
Build and Deploy Qingshuige / build-deploy (push) Successful in 1m30s
Details

Browse Source
This commit is contained in:
xianliticn
2026-04-16 21:22:20 +08:00
parent e8c7d99150
commit d13605500d
1 changed files with 2 additions and 2 deletions
Download Patch File Download Diff File Expand all files Collapse all files

4
content/blog/使用归纳法证明二项式定理.md
View File

@@ -22,14 +22,14 @@ $$
试图使左右两边相等，需要使得左边分母为$k!(n+1-k)!$，所以通分得： 试图使左右两边相等，需要使得左边分母为$k!(n+1-k)!$，所以通分得：
$$ $$
\begin{align} \begin{align*}
& \frac{n!}{(k-1)!(n-k+1)!} + \frac{n!}{k!(n-k)!} \\\\ & \frac{n!}{(k-1)!(n-k+1)!} + \frac{n!}{k!(n-k)!} \\\\
&= \frac{n!k}{k!(n-k+1)!} + \frac{n!(n-k+1)}{k!(n-k+1)!} \\\\ &= \frac{n!k}{k!(n-k+1)!} + \frac{n!(n-k+1)}{k!(n-k+1)!} \\\\
&= \frac{n!k+n!(n-k+1)}{k!(n-k+1)!} \\\\ &= \frac{n!k+n!(n-k+1)}{k!(n-k+1)!} \\\\
&= \frac{n!(n+1)}{k!(n-k+1)!} \\\\ &= \frac{n!(n+1)}{k!(n-k+1)!} \\\\
&= \frac{(n+1)!}{k!(n+1-k)!} \\\\ &= \frac{(n+1)!}{k!(n+1-k)!} \\\\
&= \binom{n+1}{k}. \tag*{$\blacksquare$} &= \binom{n+1}{k}. \tag*{$\blacksquare$}
\end{align} \end{align*}
$$ $$
随后证明二项式定理 随后证明二项式定理