I am attempting to prove that given a series of rational numbers $p/q$ as presented below: $$ 1/1,\; 2/1,\; 1/2,\; 3/1,\; 2/2,\; 1/3,\; 4/1,\; 3/2,\; 2/3,\; 1/4,\; \ldots $$
That $p/q$ is the $[(1/2)(p+q-1)(p+q-2)+q]$th term of the series.
I initially began attempting to construct the proof by induction, first setting $p=q=1$ and then $=q=n$ and so on, however, I was not able to get a solid answer.
Expanding the equation did not provide any helpful insights either.
I am wondering if anyone can provide any assistance?