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
In: 4
Don’t think of it as half the time LESS, think of it as half the time LEFT. Thus, no matter how many rooms there are, you never use all of the time available.
The maid starts with 60 seconds left to clean all the rooms. Half of the time left is 30 seconds so, for the first room, she takes 30 seconds. Now there’s 30 seconds left so for the second room, she takes 30/2 = 15 seconds. Repeat and repeat as often as you like, but you never actually take ALL of the time left. She’ll get ever closer to that one minute mark but would never actually reach it.
Latest Answers