Ch B.

asked • 08/01/19

If you're 8 feet away from a door and with each move you advance half the distance to the door. How many moves will it take to reach the door?

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Anthony B. answered • 08/01/19

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An infinite amount of moves to reach the door.

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Keith B.

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The summation of the series 1/2 + 1/4 + 1/8 + 1/16... (represented as the summation of 1/2^N from N=1 to infinity) IS equal to 1, as it is convergent. It would take an infinite amount of steps to reach the door, but you would get there. It is misleading to state that you will "never" reach the door because that would mean 1/2 + 1/4 + 1/8... =/= 1.
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08/02/19

Anthony B.

You’re right that the series is convergent to 1 but you’re not summing up the remaining distances from the door. An infinite amount of steps is synonymous to stepping half the distance forever, which would result in never reaching the door.
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08/02/19

Mark M.

The sum of the series is equal to 1 iff you do not stop adding to determine if it is equal to 1! That is the nature of "to infinity," i.e., never stopping! Look up the paradox of Xeno (Achilles and the Tortoise).
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08/02/19

Marc N.

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You're all wrong. The answer depends on the reach of the person's arm.
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08/02/19

Stephen C.

Haha! :-)
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08/03/19

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