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Theoretically forever, since there are an infinity of halves mathematically. In actuality though, with words it gets ridiculous, because it's pointless to read half of a sentence, and you really can't read half of a word, or half of a letter, so eventually you will read the whole thing.

Looking at the timeline below, if you really, really cared about going down by a half each time, you might be able to make it possibly two weeks. But if it is a good book, you are going to want to finish it much more quickly... and even if you are trying to prove a point, once you start hitting the fraction-of-a-page days starting with day 8, it gets pretty ridiculous from there.

1st day: read 120 pages -- Total 120

2nd day: read 60 pages -- Total 180

3rd day: read 30 pages -- Total 210

4th day: read 15 pages -- Total 225

5th day: read 7.5 pages -- Total 232.5

6th day: read 3.75 pages -- Total 236.25

7th day: read 1.875 pages -- Total 238.125

8th day: read .9375 pages -- Total 239.0625

9th day: read .46874 pages -- Total 239.53124

10th day: read .23437 pages -- Total 239.76561

11th day: read .117185 pages -- Total 239.882795

12th day: read .0585925 pages -- Total 239.9413875

13th day: read .02929625 pages -- Total 239.97068375

14th day: read .014648125 pages -- Total 239.985331875

15th day: read .0073240625 pages -- Total 239.9926559375

At this point, no matter how long or complex the page in an actual book, you are getting into fractured sentences and words, and in actual reading you are done. So while the mathematical theory says this continues forever, even the most dedicated actual person reading could not continue the pointless exercise any further.

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Q: You begin reading a book 240 pages long If you read half of the remaining book each day how long would it take you to finish the book?
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