Expert: Sherman D. - 2/18/2005

Question
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Followup To
Question -
I'm not good at explaining things so i will give an example.
I'm facing a wall 10 meters away.
I take a single 1 meter step.
then a 50cm step
then a 25cm step. and so on.
doing that forevor will I ever reach that wall or even get to 5 meters?
Thanks in advance.
Answer -
since you took a 1 meter step, then 50cm, then 25cm, your next steps would be 12.5, 6.25cm, 3.125, 1.5625, .78125, etc... add those together, and you will be closer to 2 meters from the wall than 5 meters.
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i must of not explained it clearly. adding 50% of the last step FOREVER will it EVER get to 10meters or even 5 meters.

Answer
Let me get this straight, you say you stepped 1 meter from the wall, then half a meter or 50cm, then stepped half of 50cm or 25cm, and so on, well if you add 1 meter, then add 50cm or .50 meters, then add 25cm or .25cm, and so on

so when i said 1 meter, 50cm, 25cm, 12.5cm 6.25cm, 3.125cm, 1.5625cm, .78125cm

what i mean is

1m, .50m, .25m, .125m, .0625m, .03125m, .015625m, .0078125m, and so on

you add all of those together, and keep adding them, you will get 1.99999999 infinity which never actually gets to 2

subtract that from 10 and you get that you are only about 8 meters from the wall, and you will never get to the 5meters or even get within 7 meters from the wall.

and when i said "your next steps would be" what i mean is if you can halving from the distance you traveled before, it would be that.

If you had traveled 2.5 meters instead of 1 meter, and then followed the same rule, you would be 4.999999 meters from the wall.

By the way, if you traveld 1 meters, then 50cm, you would add those two distance together, and you would get that you traveled 1.5meters, that is why i added the distance traveled to the distance traveled before it.