I have a remarkable plant. It grows very rapidly, you see. At the end of the first day it had increased its hei?

I have a remarkable plant. It grows very rapidly, you see. At the end of the first day it had

increased its height by a factor of 1/2. At the end of the second day it had increased its height

by a factor of 1/3 beyond where it was at the end of the first day. At the end of the third day

it had increased its height by a factor of 1/4

beyond where it was at the end of the second day.

This pattern continues, so that by the end of the n-th day, the plant has increased its height

by a factor of 1/n+1 beyond where it was at the end of the day before. How many days did it

take to grow to one hundred times its original height?

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