Positive rational numbers may be arranged in the form of a simple series: $\displaystyle \frac{1}{1}, \frac{2}{1}, \frac{1}{2}, \frac{3}{1}, \frac{2}{2}, \frac{1}{3}, \frac{4}{1}, \frac{3}{2}, \frac{2}{3}, \frac{1}{4}, ...$ Show that $\displaystyle \frac{p}{q}$ is the $\displaystyle [\frac{1}{2}(p+q-1)(p+q-2)+q]^t^h$ term of the series.

I have already considered arithmetic sequences for p and q but I don't think it works. How should I approach the problem?

Thanks.