From d316f0d8dcf54395748c1cf9b68f881f80933e65 Mon Sep 17 00:00:00 2001 From: xianliticn Date: Thu, 16 Apr 2026 21:16:57 +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 a647cf2..3b962b0 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 @@ -23,7 +23,7 @@ $$ $$ \begin{aligned} -& \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+n!(n-k+1)}{k!(n-k+1)!} \\ &= \frac{n!(n+1)}{k!(n-k+1)!} \\ @@ -44,7 +44,7 @@ $$(a+b)^0 = 1 = \sum_{k=0}^{0}\binom{0}{k}a^{0-k}b^k = a^0b^0.$$ $$ \begin{aligned} -&= (a+b)^{n+1} \\ +& (a+b)^{n+1} \\ &= (a+b)(a+b)^n \\ &= (a+b) \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k \\ &= \sum_{k=0}^{n} \binom{n}{k} (a^{n+1-k}b^k + a^{n-k}b^{k+1}) \\