There is a fertilizer that makes plants grow fast. When you apply this fertilizer, the plant will increase its height by one-half on the first day. On the second day its height increases by one-third of its height of the previous day. On the third day its height increases by one-fourth of its height of the previous day, and so on. How many days does it take to grow to 100 times its original height?
[Problem submitted by Juergen Pahl, LACC Professor of Mathematics.]
Solution for Problem 4:
Let = original height. Then
after one day the height is
after two days the height is
after three days the height is
after four days the height is , etc.
Every day the plant grows by a fixed amount of one half of its original size. Therefore,
after days its height is .