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?
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.