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authorsyn <isaqtm@gmail.com>2020-02-04 10:43:26 +0300
committersyn <isaqtm@gmail.com>2020-02-04 10:43:26 +0300
commit9d3ced22f7363af083aa82a7129ed1203957737c (patch)
treee3d923df7c1fefbb42199f8443d4f92deadd8c73
parent8af2046bf8bbcb512b6040ca15079ca9618d37a4 (diff)
downloadtex2-9d3ced22f7363af083aa82a7129ed1203957737c.tar.gz
Couple fixes
-rw-r--r--dm-14.tex6
1 files changed, 3 insertions, 3 deletions
diff --git a/dm-14.tex b/dm-14.tex
index cb48628..313e693 100644
--- a/dm-14.tex
+++ b/dm-14.tex
@@ -21,7 +21,7 @@
\twocolumn
\begin{center} \textbf{1} \end{center}
- По условию, $\expected{\text{prize}} = 40$
+ По условию, $\expected{\textrm{prize}} = 40$
Значит,
\[
\expected{\text{prize} \geqslant 5000} \leqslant \frac{40}{5000} < 0.01
@@ -104,8 +104,8 @@
A_n = \frac{(100n)!}{(99n)! (100n)^n} &=\\
\frac{99n + 1}{100n} \cdot \ldots \cdot \frac{99n + n}{100n} &=\\
\frac{99n + 1}{100n} \cdot \ldots \cdot \frac{99n + \frac{n}{2}}{100n} \cdot Q_n &\leqslant \qquad\qquad Q_n < 1\\
- \braced{ \frac{99n + \frac{n}{2}}{100n} }^{\frac{n}{2}} Q_n =
- \braced{ \frac{99.5}{100} }^{\frac{n}{2}} Q_n = B_n
+ \br{ \frac{99n + \frac{n}{2}}{100n} }^{\frac{n}{2}} Q_n =
+ \br{ \frac{99.5}{100} }^{\frac{n}{2}} Q_n = B_n
\end{flalign*}
$\displaystyle \lim_{n \to \infty} B_n = 0$, а так как $0 < A_n \leqslant B_n$, то
$\displaystyle \lim_{n \to \infty} A_n = 0$, что и требовалось