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Update Math401_P1_3.md

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Zheyuan Wu
2025-07-23 16:08:09 -05:00
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@@ -191,7 +191,7 @@ $$
as $n\to \infty$. as $n\to \infty$.
note that $\lim_{n\to \infty}{1-\frac{a}{n}}=e^{-a}$ for any $a>0$. note that $\lim_{n\to \infty}{(1-\frac{a}{n})^n}=e^{-a}$ for any $a>0$.
$(n-\|x\|^2)^{\frac{n-k}{2}}=\left(n(1-\frac{\|x\|^2}{n})\right)^{\frac{n-k}{2}}\to n^{\frac{n-k}{2}}\exp(-\frac{\|x\|^2}{2})$ $(n-\|x\|^2)^{\frac{n-k}{2}}=\left(n(1-\frac{\|x\|^2}{n})\right)^{\frac{n-k}{2}}\to n^{\frac{n-k}{2}}\exp(-\frac{\|x\|^2}{2})$