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 .