From 1de9c3decb33c85b06625e9fb9abb60d2261fd28 Mon Sep 17 00:00:00 2001
From: Barrett Ruth <barrett.ruth@ramp.com>
Date: Sun, 9 Nov 2025 15:07:46 -0500
Subject: [PATCH] fix(proofs): reformat equation to be multiline

---
 src/content/algorithms/proofs.mdx | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/content/algorithms/proofs.mdx b/src/content/algorithms/proofs.mdx
index ad7c189..c770058 100644
--- a/src/content/algorithms/proofs.mdx
+++ b/src/content/algorithms/proofs.mdx
@@ -83,9 +83,9 @@ As $S_i<S_{j>i}$, $|S_{j>i}-S_i|=S_{j>i}-S_i$--the sum is unchanged. Rewriting t
 
 $$
 \begin{align*}
-\sum_{1\leq r\leq n}\sum_{1\leq l<r} |X-Y| &=\sum_{1\leq r\leq n}\sum_{1\leq l<r}S_r-\sum_{1\leq r\leq n}\sum_{1\leq l<r}S_l
-&=\sum_{1\leq r\leq n}r\cdot S_r-\sum_{1\leq l<r\leq n} S_l
-&=\sum_{1\leq r\leq n}r\cdot S_r-\sum_{1\leq r\leq n} (n-r)\cdot S_r
+\sum_{1\leq r\leq n}\sum_{1\leq l<r} |X-Y| &= \sum_{1\leq r\leq n}\sum_{1\leq l<r}S_r-\sum_{1\leq r\leq n}\sum_{1\leq l<r}S_l \\
+&= \sum_{1\leq r\leq n}r\cdot S_r-\sum_{1\leq l<r\leq n} S_l \\
+&= \sum_{1\leq r\leq n}r\cdot S_r-\sum_{1\leq r\leq n} (n-r)\cdot S_r
 \end{align*}
 $$