Posted by tpc at January 24th, 2009

I was reading this light-hearted article by jeremy au yong in the local papers. It’s mainly about how the economy is bad and he was retrenching his girlfriend. As compensation he offered a gift.

The value of this gift will be determined by using the formula $15 x years of service + cube root of pi, differentiated over the limit of zero to infinity.

Something is wrong right? Does he mean integrated rather than differentiated, since nobody differentiates over a range. As the only variable is y for years of service, does he mean
\displaystyle \int_0^\infty (15 y + \sqrt[3]\pi ) dy = \infty.

Well, how does one pay off this infinite debt? Once again, mathematics to the rescue. He can pay his girlfriend 1 cent today, 1/2 cent tomorrow and 1/3 cent the day after …
\displaystyle \sum_{n=1}^\infty \frac{1}{n} = \infty.