$$ \sum_{p \, \in \text{ primes}} \frac{1}{2^p} $$
My friend came across a book which claimed this to be irrational and claimed it could be solved using the pigeonhole principle.
Is $\sum_{p} \frac{1}{2^p}$ irrational?
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sequences-and-series
prime-numbers
pigeonhole-principle
rationality-testing
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4Well, the pigeonhole principle is used to prove that any rational number, when written in any base $b$, either terminates or repeats. This number, when written in base $2,$ does not terminate nor repeat. – 2017-01-05
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0Dear Agnishom. You should first check the related questions (right margin), before posing a question. – 2017-01-05
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1What do you think about the number $0.011010100010100010100010000010_2\cdots$ ? – 2017-01-05