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4/3/2013 3:22:54 AM
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Infinite series question

Ok, in the above series, it equals 1. You get there by adding .9+.09+.009... and so on. My question is, does it actually equal 1 or is it an approximation? I don't need to know this for any particular reason, just doing my homework and got to thinking. :P
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  • Edited by Uncle Putin: 4/3/2013 3:31:58 AM
    It depends on how you view infinity. If you see infinity as this exact quantity, then it does equal 1. If you view infinity as this never ending number that continuously gets bigger and bigger, then no, it does not equal 1. There are some people out there that would try to argue with you that the series you gave really does equal 1, but I'm not so sure it's true. Let's say there's a marathon going on in your home town. Runner number 74 has this rare condition that allows him to only run half of a distance at a time. So when the race starts, he gets to the halfway mark and then stops. He takes a 2 minute break and then starts running again. However, he gets tired again when he hits the 3/4ths mark, so he waits two minutes and then starts again. However, he gets tired AGAIN and only makes it to the 7/8ths mark. He keeps doing this over and over again into infinity. He never crosses the line because he's always going half of the distance that he needs to. He gets closer and closer, but he never gets there because he's always going half the distance. The same thing applies to your series. The runner is always getting 9/10ths of the way to the finish line, but he just never gets there. I don't know if that helps you, but that's the best I can explain it.

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