Earlier this month (December 1), the 68th William Lowell Putnam Mathematical Competition was held at universities throughout the United States and Canada. In commemoration, this month's problem is from a previous Putnam.

You open a bank account that pays an interest rate of *r* compounded annually.
What is the minimum amount of money you can invest (as a function of *r*)
so that you can withdraw $1
at the end of the first year, $4 at the end of the second year, ...
*n*^{2} dollars at the end of the *n*^{th}, etc., etc.?