Ive just watched the Netlfix documentary called A Trip To Infinity, they mentioned the very famous infinity hotel paradox but with something extra i have not heard yet.. they said the maid is done checking all the rooms in the infinite hotel in ONE MINUTE, by taking half the time less in the next room. 30 seconds in room 1, 15 seconds in room 2, 7,5 seconds in room 3. So 1/2 + 1/4 + 1/8…….. + 1/infinity equals ONE. Could someone please explain the math behind this, thank you
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With infinite series, if the series has a limit, then the series is equal to that value. The limit of 1/2 + 1/4 + 1/8… is 1, and so the infinite series equals 1. If the series has no limit, then it is equal to infinity.
A fun (controversial) series is the sum of all natural numbers. 1 + 2 + 3… It has no limit, and therefore should be equal to infinity, but there are proofs that prove it equals -1/12. Some advanced physics only work if the answer is -1/12, so that HAS to be the answer. But how do you get a negative fraction by adding positive whole numbers? Infinity is fun.
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