Can this decimal with special patterns be expressed as a fraction? Is it a rational number?
$$0.101001000100001000001...$$
Where the number of zeros after every 1 is increased by 1.
Ty.
2026-04-01 02:00:29.1775008829
Representing a strange number as a fraction
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It is an irrational number, since it does not have a periodic decimal expansion. Hence it cannot be expressed as a fraction of two integers.