Difference between revisions of "MR 03 Lösung rlk"
(Link to problem statement.) |
(Added Fibonacci construction.) |
||
| Line 2: | Line 2: | ||
=Die folgenden 14 Ausdrücke haben den Wert 50= | =Die folgenden 14 Ausdrücke haben den Wert 50= | ||
| − | ==Verschiedenes ( | + | ==Verschiedenes (6)== |
<math>2\cdot 5^2</math><br> | <math>2\cdot 5^2</math><br> | ||
<math>7^2+1</math><br> | <math>7^2+1</math><br> | ||
| Line 9: | Line 9: | ||
<math>\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left(\left(\left(1+1+1\right)!\right)!\right)!}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor | <math>\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left(\left(\left(1+1+1\right)!\right)!\right)!}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor | ||
</math> [[http://home.pipeline.com/~hbaker1/hakmem/number.html#item34| HAKMEM #34]] <br> | </math> [[http://home.pipeline.com/~hbaker1/hakmem/number.html#item34| HAKMEM #34]] <br> | ||
| + | <math>\left\lfloor\frac{\phi^{10}-\phi^{5}}{\sqrt{5}}\right\rfloor</math> mit dem Verhältnis <math>\phi=\frac{1+\sqrt{5}}{2}</math> des goldenen Schnitts<br> | ||
==Grenzwerte (3)== | ==Grenzwerte (3)== | ||
Revision as of 13:05, 15 April 2014
Diese Lösung für MR_03 ist noch nicht vollständig, ich habe noch nicht alles eingetippt, was ich mir überlegt habe und ich denke weiter nach...
Die folgenden 14 Ausdrücke haben den Wert 50
Verschiedenes (6)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\cdot 5^2}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7^2+1}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{(\sin(\arccot(7))^2}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2(4!+1)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left(\left(\left(1+1+1\right)!\right)!\right)!}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor }
[HAKMEM #34]
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left\lfloor\frac{\phi^{10}-\phi^{5}}{\sqrt{5}}\right\rfloor}
mit dem Verhältnis Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi=\frac{1+\sqrt{5}}{2}}
des goldenen Schnitts
Grenzwerte (3)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to 0}\frac{\sin(100 x)}{2 x}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to 0}150\cdot\frac{\sinh(x)-\sin(x)}{x^3}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to 0}100\cdot\frac{\tan(x)-\sin(x)}{x^3}}
Summen (4)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=0}^\infty\left(\frac{49}{50}\right)^n}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=-\infty}^\infty\left(\frac{7^2}{51}\right)^{|n|}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3+\sum_{p\in\mathbb{P}\land p\leq 17}(p-3)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ln(e)+\sum_{n=0}^{\infty}n\left (\frac{6}{7}\right)^{n+\exp(\mathbf{i}\pi)}}
Integrale (2)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \displaystyle\int_1^{e^{50}}\frac{1}{x}\,\mathrm{d}x}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_0^\pi\sin(x)\,\mathrm{d}x \cdot\int_0^\sqrt{10} y \cdot y \cdot y \,\mathrm{d}y}