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, ... n2 dollars at the end of the nth, etc., etc.?