Daleth function (Martinez)

The daleth function, as described by Gilbert Martinez on 27 Sep 2018, allows one to compute the sum of any geometric series.

$\daleth (a, r) = a \sum_{n=0}^{\infty} r^{n} = \frac{at}{t-s} \iff |r| < 1 \and r = \frac{s}{t}$

Here, a is the first term of the series, and r is the fraction that is exponentially multiplied to each term.

$a \sum_{n=0}^{\infty} r^{n} = a + ar + ar^{2} + ar^{3} + ...$

Here are a few examples of the daleth function in action.

$\daleth (1,{\frac {1}{2}})=\sum _{n=0}^{\infty }({\frac {1}{2}})^{n}={\frac {1*2}{2-1}}={\frac {2}{1}}=2$

The daleth hypothesis, proposed the same day, suggests that every rational number can be computed with the daleth function, although this hasn't been proven yet.