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| author | mzuenni <mzuenni@users.noreply.github.com> | 2024-07-28 22:54:40 +0200 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2024-07-28 22:54:40 +0200 |
| commit | 8d11c6c8213f46f0fa19826917c255edd5d43cb1 (patch) | |
| tree | 96d75baff33d5a04b5a60f1a41f514a26c716874 /content/math/tables/binom.tex | |
| parent | 8c33b4e0d3030cfed17fc64b4fe41133339f6d87 (diff) | |
Test (#4)
* update
* moved content in subdir
* rename file
* add test setup
* add test setup
* add github action
* automaticly test all cpp files
* timeout after 10s
* setulimit and dont zero memory
* test build pdf
* install latexmk
* update
* update
* ngerman
* fonts
* removed old code
* add first test
* added tests
* test in sorted order
* more tests
* simplified test
* more tests
* fix suffix tree
* fixes and improvements
* done ust lst directly
* fix swap
* add links to pdf
* fix constants
* add primorial
* add comment
* various improvements
* more tests
* added missing stuf
* more tests
* fix tests
* more tests
* more tests
* more tests
* fix recursion?
* test trie
* more tests
* only use python temporarily for listings
* only use python temporarily for listings
* more tests
* fix longestCommonSubstring
* more tests
* more tests
* made code more similiar
* fix?
* more tests
* more tests
* more tests
* add ahoCorasick test + limit 4GB stack size
* more tests
* fix test
* add additional test
* more tests
* more tests
* fix?
* better fix
* fix virtual tree
* more tests
* more tests
* recursive closest pair
* more tests
* decrease limit
* new tests
* more tests
* fix name
* more tests
* add test
* new test
* more tests
* more tests
* more tests
* more tests
* new test and content
* new code
* new code
* larger tests
* fix and test
* new test
* new test
* update pdf
* remove comments
* new test
* more tests
* more testcases
* more tests
* increased limit
* more tests
* more tests
* more tests
* new tests
* more tests
* shortened code
* new test
* add basic tests for bigint
* more tests
* removed old files
* new test
* ignore some files
* more auto more ccw
* fix test
* more tests
* fix
* new tests
* more tests
* more tests
* stronger test
* actually verify delaunay...
* more tests
* fix header
* more tests
* run tests parallel?
* test parralel?
* add --missing
* separate workflows
* test
* is the pdf checked?
* separate workflows
* fix workflow
* more workflows
---------
Co-authored-by: Yidi <noob999noob999@gmail.com>
Diffstat (limited to 'content/math/tables/binom.tex')
| -rw-r--r-- | content/math/tables/binom.tex | 28 |
1 files changed, 28 insertions, 0 deletions
diff --git a/content/math/tables/binom.tex b/content/math/tables/binom.tex new file mode 100644 index 0000000..878a6b0 --- /dev/null +++ b/content/math/tables/binom.tex @@ -0,0 +1,28 @@ +\begin{tabularx}{\linewidth}{|XXXX|} + \hline + \multicolumn{4}{|c|}{Binomialkoeffizienten} \\ + \hline + \multicolumn{4}{|c|}{ + $\frac{n!}{k!(n - k)!} \hfill=\hfill + \binom{n}{k} \hfill=\hfill + \binom{n}{n - k} \hfill=\hfill + \frac{n}{k}\binom{n - 1}{k - 1} \hfill=\hfill + \frac{n-k+1}{k}\binom{n}{k - 1} \hfill=\hfill + \binom{n - 1}{k} + \binom{n - 1}{k - 1} \hfill=\hfill + (-1)^k \binom{k - n - 1}{k} \hfill\approx\hfill + 2^{n} \cdot \frac{2}{\sqrt{2\pi n}}\cdot\exp\left(-\frac{2(x - \frac{n}{2})^2}{n}\right)$ + } \\ + \grayhline + + $\sum\limits_{k = 0}^n \binom{n}{k} = 2^n$ & + $\sum\limits_{k = 0}^n \binom{k}{m} = \binom{n + 1}{m + 1}$ & + $\sum\limits_{i = 0}^n \binom{n}{i}^2 = \binom{2n}{n}$ & + $\sum\limits_{k = 0}^n\binom{r + k}{k} = \binom{r + n + 1}{n}$\\ + + $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n - k}{m - k}$ & + $\sum\limits_{k = 0}^n \binom{r}{k}\binom{s}{n - k} = \binom{r + s}{n}$ & + \multicolumn{2}{l|}{ + $\sum\limits_{i = 1}^n \binom{n}{i} F_i = F_{2n} \quad F_n = n\text{-th Fib.}$ + }\\ + \hline +\end{tabularx} |