Magic tree

Question:

There was a magic tree that on the first day increased its height by half, on the second by day by a third, on the third day by a quarter, and so on. How many days did it take it to grow one hundred times its original height?

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Solution: It will take 198 days. Let’s say the tree was originally one foot tall. On the first day, it grew half a foot; on the next day 1⁄3 of 11⁄2 feet, which is half a foot; and so on – it grew half a foot every day. So in 198 days, it grew 99 feet and then was 100 feet tall.

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