Termial/Examples/Half
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Example of Termial
The termial of $\dfrac 1 2$ is given by:
- $\dfrac 1 2 ? = \dfrac 3 8$
Proof
By definition of termial:
| \(\ds \dfrac 1 2 ?\) | \(=\) | \(\ds \frac {\frac 1 2 \paren {\frac 1 2 + 1} } 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 2 \times \dfrac 1 2 \times \dfrac 3 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 3 8\) |
$\blacksquare$
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.5$: Permutations and Factorials