Mathematics

Miscellaneous

Phi (\(\phi\)) is the golden ratio.

\({\Large \phi = \frac{ 1 + \sqrt{5} }{2}}\)


Look into Toads and Frogs game. See OEIS “A005563 a(n) = n*(n+2) = (n+1)^2 – 1″ or OEIS search for “frog”.


Numbers

818

Notation

\({}^n C {}_r\) — N Choose R

\({}^n C {}_r\) (“n choose r”) is an alternate notation for the binomial symbol:
$${}^n C {}_r = {n \choose r} = \frac{n!}{r!(n−r)!}$$

\({}^n C _r\) is an alternate notation for the binomial symbol \({n \choose r} = \frac{n!}{r!(n−r)!}\)

Inline style: \({}^{10}C_{3} = {10 \choose 3} = \frac{10!}{3!(10−3)!} = \frac{10!}{3! 7!} = \frac{3628800}{6×5040} = \frac{3628800}{30240} = 120\)
\({}^{10}C_{3} = {10 \choose 3} = \frac{10!}{3!(10−3)!} = \frac{10!}{3! 7!} = \frac{3628800}{6×5040} = \frac{3628800}{30240} = 120\)

Display style: $${}^{10}C_{3} = {10 \choose 3} = \frac{10!}{3!(10−3)!} = \frac{10!}{3! 7!} = \frac{3628800}{6×5040} = \frac{3628800}{30240} = 120$$
$${}^{10}C_{3} = {10 \choose 3} = \frac{10!}{3!(10−3)!} = \frac{10!}{3! 7!} = \frac{3628800}{6×5040} = \frac{3628800}{30240} = 120$$

\(\sum_{n=1}^{\infty}\) — Summation

Inline style: \(\sum_{n=1}^{\infty} 2^{-n} = 1\)
\(\sum_{n=1}^{\infty} 2^{-n} = 1\)

Display style: $$\sum_{n=1}^{\infty} 2^{-n} = 1$$
$$\sum_{n=1}^{\infty} 2^{-n} = 1$$

Inline style: \(\sum\limits_{k=1}^{n} k\)
\(\sum\limits_{k=1}^{n} k\)

Display style: $$\sum\limits_{k=1}^{n} k$$
$$\sum\limits_{k=1}^{n} k$$


See Also

Xcas, the swiss knife for mathematics. Giac/Xcas is a free computer algebra system for Windows, Mac OS X and Linux/Unix.

Use Xcas online in your web browser.

References

Alekseyev, Max. “PARI/GP Scripts for Miscellaneous Math Problems“. George Washington University.

De Graeve, Renée; Parisse, Bernard. “Symbolic Algebra and Mathematics with Xcas“. University of Grenoble I.

MathJax TeX and LaTeX Support“. MathJax Consortium.

Wikipedia contributors. “List of computer algebra systems“. Wikipedia.

Footnotes

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