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author | syn <isaqtm@gmail.com> | 2020-02-04 10:43:26 +0300 |
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committer | syn <isaqtm@gmail.com> | 2020-02-04 10:43:26 +0300 |
commit | 9d3ced22f7363af083aa82a7129ed1203957737c (patch) | |
tree | e3d923df7c1fefbb42199f8443d4f92deadd8c73 | |
parent | 8af2046bf8bbcb512b6040ca15079ca9618d37a4 (diff) | |
download | tex2-9d3ced22f7363af083aa82a7129ed1203957737c.tar.gz |
Couple fixes
-rw-r--r-- | dm-14.tex | 6 |
1 files changed, 3 insertions, 3 deletions
@@ -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 |