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Results tagged with irrational-numbers
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user 105244
An irrational number is a real number that cannot be expressed in the form $\frac{n}{m}$ where $n$ and $m$ are integers.
2
votes
Irrationality of generalized continued fractions
Apparently no such extension is known. But there are other irrationality criteria for sequences of the form
$$\frac{\sum_{i=1}^n a_i}{\sum_{i=1}^n b_i},$$
such as those by Brun and by Froda.
- 201
8
votes
3
answers
689
views
Irrationality of generalized continued fractions
An infinite simple continued fraction
$$\frac{1}{b_1 + \frac{1}{b_2 + \frac{1}{b_3+\dots}}} (b_i\in\mathbb Z\setminus\left\{0\right\})$$
is irrational. Now for a generalized continued fraction:
$$\fra …
- 201